back to Illinois

Robert H. Johnson

off-topic - social media

Do the people you know on blogs affect your odds?

Algebra II Before Geometry

This is happening in our area (not at my son's HS), but I'm not sure why. Is it being driven by the CCSSO standards? Do high schools want to get most students through the material (pseudo-Algebra II) before it's too late or while the algebra "iron" is hot? If this is true, then the top math track in high school is under attack. It's one thing to channel students off to integrated math, like Core Plus, but with the current emphasis on the traditional sequence of math classes, there seems to be only one direction for the content to go. Traditional math won, but ends up losing. Is that what will happen in lower schools if they decide to use Singapore Math? Perhaps I'm reading too much into this. I don't have any strong feelings about whether geometry or algebra II should come first, but I do have strong feelings about rigor. What is the real driving force behind the switch? Do they use the same textbooks? One comment I heard once was that this would allow the geometry classes to delve more deeply into proofs because the students would be more mature and would have more math background. I don't buy it. What direction would algebra II go, even for the honors version?

Knowledge is good

Just heard from Barry - new article from Sweller, Clark, & Kirschner is out --

Problem solving is central to mathematics. Yet problem-solving skill is not what it seems. Indeed, the field of problem solving has recently undergone a surge in research interest and insight, but many of the results of this research are both counterintuitive and contrary to many widely held views. For example, many educators assume that general problem-solving strategies are not only learnable and teachable but are a critical adjunct to mathematical knowledge. The best known exposition of this view was provided by Pólya (1957)....[I]n over a half century, no systematic body of evidence demonstrating the effectiveness of any general problem-solving strategies has emerged. It is possible to teach learners to use general strategies such as those suggested by Pólya (Schoenfeld, 1985), but that is insufficient.

[snip]

The alternative route to acquiring problem-solving skill in mathematics derives from the work of a Dutch psychologist, De Groot (1946–1965), investigating the source of skill in chess. Researching
why chess masters always defeated weekend players, De Groot managed to find only one difference. He showed masters and weekend players a board configuration from a real game, removed it after five seconds, and asked them to reproduce the board. Masters could do so with an accuracy rate of about 70% compared with 30% for weekend players. Chase and Simon (1973) replicated these results and additionally demonstrated that when the experiment was repeated with random configurations rather than real-game configurations, masters and weekend players had equal accuracy (±30%). Masters were superior only for configurations taken from real games.

[snip]

The superiority of chess masters comes not from having acquired clever, sophisticated, general problem-solving strategies but rather from having stored innumerable configurations and the best moves associated with each in long-term memory.

[snip]

[L]ong-term memory, a critical component of human cognitive architecture, is not used to store random, isolated facts but rather to store huge complexes of closely integrated information that results in problem-solving skill. That skill is knowledge domain-specific, not domain-general. An experienced problem solver in any domain has constructed and stored huge numbers of schemas in long-term memory that allow problems in that domain to be categorized according to their solution moves.

[snip]

[D]omain-specific mathematical problem-solving skills can be taught. How? One simple answer is by emphasizing worked examples of problem-solution strategies. There is now a large body of evidence showing that studying worked examples is a more effective and efficient way of learning to solve problems than simply practicing problem solving without reference to worked examples (Paas & van Gog, 2006).

[snip]

For novice mathematics learners, the evidence is overwhelming that studying worked examples rather than solving the equivalent problems facilitates learning. Studying worked examples is a form of direct, explicit instruction that is vital in all curriculum areas, especially areas that many students find difficult and that are critical to modern societies. Mathematics is such a discipline. Minimal instructional guidance in mathematics leads to minimal learning (Kirschner, Sweller, & Clark, 2006).

Teaching General Problem-Solving Skills Is Not a Substitute for, or a Viable Addition to, Teaching Mathematics (pdf file)
by John Sweller, Richard Clark, and Paul Kirschner

the Arizona case

School Choice on Trial

punctuating by breath

from Sentence Diagramming: A Step-by-Step Approach to Learning Grammar Through Diagramming:

Before the 1960s, grammar and punctuation were taught as foundation blocks for writing instruction. In the 1960s, some research questioned the value of teaching grammar, and new ways of teaching grammar cast doubt on the traditional methods. In the midst of all this change, the baby was thrown out with the bath water where grammar was concerned, and when the 1970s rolled around, a new generation of teachers had not been trained to teach grammar and punctuation.

I am a member of that new generation of teachers, and a product of a writing education with little structured or sustained lessons in grammar. Thankfully, one of my teachers believed in teaching grammar and punctuation through sentence diagramming. Before this instruction, I lacked confidence in my writing because I didn't know for sure if my sentences were really sentences.

I can still remember the great "aha!" feeling I had when I realized that I could analyze a sentence without the teacher's assistance--I could mentally diagram the sentence to determine if it was grammatically correct. What a sense of power that gave me!

Marye Hefty

I find this remarkable.

Mary Hefty earned a Masters degree in English and then worked as an editor in a research laboratory, but as a child (or teen?) she could not tell whether she had or had not written a sentence.

Crazy!

She goes on:

When I left the research laboratory to become a college professor, teaching English composition and technical writing, I noticed during the first term that many of my students' papers were riddled with grammar and punctuation errors. I didn't know how to add the necessary instruction in grammar and punctuation skills to our limited class time without letting it take over the class like a weed. Typically, I tried a band-aid approach to teaching grammar and punctuation. When I saw sentence fragments in the students' papers, I talked about sentence fragments. When I saw comma splices, I talked about those. It didn't take long to realize that many of my students didn't recognize a sentence, so they couldn't solve the sentence problems. My students were just like I had been--needing structure and an organized way to learn grammar and punctuation without having the approach overwhelm them or make it difficult for them to learn the writing process in class.

In several classes, I decided to discard the band-aid approach and devote 10 percent of the class time to teaching the students grammar and punctuation, starting with the basics--What is a simple sentence? How do you diagram it? And guess what? It worked.

I've been teaching sentence diagramming in some of my courses for eight years now, and the students who begin my classes not being able to identify or define a simple sentence leave the class with the vocabulary and knowledge to identify simple, compound, and complex sentences; fragments; run-ons; and comma splices. Most importantly, the students have a foundation that enables them to learn more--without my help--after they leave the class.

Surprisingly, my university students don't mind having to learn grammar and punctuation through sentence diagramming because this approach quickly gives them the skills and confidence to fix the problems in their papers on their own. I have heard enough anecdotal evidence from my students to know that sentence diagramming works. For example, one of my former students told me that she was asked to edit letters for her boss. She said that before taking my class, she just put in the commas in where she thought she heard a pause and just guessed that the sentences were correct. "Now I know for sure, and I can really help," she said.

A lot of my students -- these are college freshmen -- "punctuate by breath."

Punctuating by breath is OK as far as it goes, I think. Now that I'm learning the formal rules of punctuation, I realize I've been breaking some of those rules for decades. I've been breaking the rules because a) I didn't know them, so b) I've been punctuating by breath.

Having thought it over, I've decided to carry on punctuating by breath when the occasion calls for it. If I want or don't want a comma somewhere,  then a comma there will or will not be. I'm the decider.

Still and all, the reason this works for me is that I have never, ever, in my entire adult life, failed to recognize a complete sentence. Nor have I failed to write a complete sentence if that's what I wanted to write.

I have come to the realization that a course about writing is a course about sentences.

Time

My dad died this week.

Didn't see it coming.

My mom reminded me that she and my dad stayed at our house when I was pregnant with the twins. Or maybe it was right after I had the twins, I don't remember. Every morning, Jimmy would get in bed with them and wake my dad, whom we all called Bob, because that was his name. We called my mom Pat & my dad Bob.

After a few days, Bob left to go back home and my mom stayed on.

Every morning after that, Jimmy would get in bed with my mom and chant, "No more Bob, no more Bob."

Back to Illinois on the weekend for the funeral.

Preconceived notions about place value

(Cross-posted at Out in Left Field--with some great comments)

One thing that struck me about the math talks given at this weekend's New England Conference on the Gifted and Talented was the emphasis on manipulatives and the concerns about whether children understand place value. Are these the most appropriate things to be focusing on when it comes to students who are gifted in math? The mathematically gifted kids I know grasp place value and other aspects of arithmetic with only minimal exposure to manipulatives, and quickly advance to higher levels of abstraction by the time they hit first or second grade. But the education establishment seems bent on convincing itself that children--however gifted--don't understand place value.

Why would you want to convince yourself of this? Because it gives you an excuse not to teach the standard algorithms of arithmetic. If children don't understand place value, then they can't understand borrowing and carrying (regrouping), let alone column multiplication and long division. And unless they understand how these procedures work from the get-go, educators claim (though mathematicians disagree), using them will permanently harm their mathematical development.

So, given how nice it would be not to feel any pressure to teach the standard algorithms (because, let's admit it, they are rather a pain to teach), wouldn't it nice to convince ourselves that our elementary school students, however gifted in math, don't understand place value?

But how do you convince yourself of this? As that ground-breaking math education theorist Constance Kamii has shown, it's child's play. All you have to do is ask a child the right sort of ill-formed question. Here's how it works:

1. Show the child a number like this:

27

2. Place your finger on the left-most digit and ask the child what number it is.

3. When the child answers "two" rather than "twenty," immediately conclude that he or she doesn't understand place value.

4. Banish from your mind any suspicion that a child who can read "27" as "twenty-seven" might simultaneously (a) know that the "2" in "27" is what contributes to twenty-seven the value of twenty and (b) be assuming that you were asking about "2" as a number rather than about "2" as a digit.

travelling salesman

solved by bees

metrics feel good

24/7

Sorry to be AWOL...I am CHAINED TO MY DESK!

(Teaching 2 courses I've never taught before, both of them composition & literature, which means lots of paper reading and lots of reading-reading.)

I'm doing no math at all. None. Not even the SAT Question of the Day.

I'm spending so much time on English literature, fables, folk tales, and short stories that I think I'll just start posting some of the work I'm doing there for the time being.

For starters, here's a fantastic site for English students:

Getting an A on an English paper

factoid

Spotted this in the Times Book Review last night:

Town, county and state governments no longer have much independent political identity. They are mere “conduits for federal mandates,” as Codevilla puts it. He notes that the 132 million Americans who inhabited the country in 1940 could vote on 117,000 school boards, while today a nation of 310 million votes in only 15,000 school districts.

The State of Conservatism
By CHRISTOPHER CALDWELL
Published: October 21, 2010

A couple of years ago, when busing costs were at issue here in Irvington, we learned that at some point in NY history the state 'incentivized' (hate that word) districts to consolidate by picking up some of the transportation costs. I no longer recall the details, and the story doesn't make sense given the fact that the town is paying transportation costs, not the state.

But I'm pretty sure the state-incentivizing part is correct in some way, and it's interesting in light of Codevilla's statistics.

help desk - sentence structure

Alicia took an earlier bus than she needed to, for she didn’t want to be late.

Is this sentence simple or complex?

Over Sixty Percent Remedial

Our state paper had an article today about how 60% of the kids entering our community college system need at least one remedial class. Fifty percent need at least 2. (I think this is true nationally.) It also says that these kids run the greatest risk of dropping out. There are other issues since the graduation rate is only 10%.

The state Education Commisioner says that "... we need more college-educated adults ..." and that "...even if they don’t go to college, they need a level of skills to be successful in life." and also “We have to understand that this builds over time, from the very first day of elementary school, ...”.

The community college gives a standard test to all incoming freshman. The state tests (K-12) align with this standard (it's pretty low), but K-12 schools still allow students to move on to the next grade without meeting the low proficiency grade-level cutoffs. What do they think is going to happen? If they place the entire onus of success in education on the kids (and parents), then how do they think they are going to fix the problem?

spelling alone

Deliberate Practice Spells Success: Why Grittier Competitors Triumph at the National Spelling Bee

Barry G on the Times story

The New York Times ran a story on September 30 about Singapore Math being used in some schools in the New York City area.  Like many newspaper stories about Singapore Math, this one was no different.  It described a program that strangely sounded like the math programs being promoted by reformers of math education, relying on the cherished staples of reform: manipulatives, open-ended problems, and classroom discussion of problems.  The only thing the article didn’t mention was that the students worked in small groups.

[snip]

The mistaken idea that gets repeated in many such articles is that Singapore Math differs from other programs by requiring or imparting a “deep understanding” and that such understanding comes about through a) manipulatives, b) pictures, and c) open-ended discussions.  In fact, what the articles represent is what the schools are telling the reporters. What newspapers frequently do not realize when reporting on Singapore Math, is that when a school takes on such a program, it means going against what many teachers believe math education to be about; it is definitely not how they are trained in ed schools.  The success of Singapore’s programs relies in many ways on more traditional approaches to math education, such as explicit instruction and giving students many problems to solve, in some ways its very success represented a slap in the face to American math reformers, many of whom have worked hard to eliminate such techniques being used.

[snip]

Singapore’s strength is the logical consistency of the development of mathematical concepts. And much to the chagrin of educators who may have learned differently, mastery of number facts and arithmetic procedures is part and parcel to conceptual understanding.  Starting with conceptual understanding and using procedures to underscore it is an invitation to disaster—such approach is making profits for  outfits like Sylvan, Huntington and Kumon.

[snip]

Fortunately, the logical structure and word problems in Singapore’s books are so good it will work in spite of the disciples of reform.  My friend is right.  If the education community wants to think that Singapore Math is student-centered and inquiry-based and the realization of US reforms, let them think it.  For those of us who know better, it will remain our dirty little secret.
Singapore Math Is “Our Dirty Little Secret”

Waiting for Superman

cross posted to the Irvington Parents Forum

Waiting for Superman

Tue, October 12 5:10 || 7:25 || 9:40
Wed, October 13 5:10 || 7:25 || 9:40
Thu, October 14 5:10 || 7:25 || 9:40

Jacob Burns Film Center Theater
364 Manville Rd., Pleasantville, NY 10570
Info-line: 914.747.5555
914.773.7663

============

Hi everyone -

Waiting for Superman is incredible. So moving. Entertaining, too; Geoffrey Canada in particular is riveting. The title comes from a story he tells about the day his mother told him Superman doesn’t exist.

The film follows 5 or 6 children whose families are trying to find good schools for their kids, including one mom who can no longer afford the Catholic school her daughter has been attending. The lottery scenes at the end are excruciating.

Amazingly, the film does **not** give wealthy, white suburban schools a pass. About three quarters of the way in, the film tells us that suburban schools have the same underachievemement problems urban schools do; then we see data showing that the top 5% of U.S. students rank far below the top 5% of students in other countries. Which is true.

Here’s a picture of the suburban girl waiting to see if her number will be called:

Here’s the trailer.

Catherine

What about the US's better students? When asked, Schmidt replied, "For some time now, Americans have comforted themselves when confronted with bad news about their educational system by believing that our better students can compare with similar students in any country in the world. We have preferred not to believe that we were doing a consistently bad job. Instead, many have believed that the problem was all those 'other' students who do poorly in school and who we, unlike other countries, include in international tests. That simply isn't true. TIMSS has burst another myth - our best students in mathematics and science are simply not 'world class'. Even the very small percentage of students taking Advanced Placement courses are not among the world’s best."

TIMSS - Trends in International Mathematics and Science Studies

MSMI for schools and homeschoolers?

In the Homeschooling by the Numbers thread, there was much back and forth critical of criticisms of homeschoolers lacking content knowledge--mostly centered around the ideas that a) schools have the same problems, and b) tailoring to one's child is a good thing.

Wrt to the first criticism, that school teachers lack content knowledge, I've created a not-for-profit corporation to address this. MSMI, the Middle School Mathematics Institute, is aimed at parents, teachers and schools serving students in grades 4-8, offering a variety of services to help build the bridge to Algebra 1.

For teachers, we offer intensive workshops, known as "institutes" that teach the math behind the school mathematics that teachers are teaching. It teaches the foundational pieces to help teachers understand that math is meant to be coherent and precise, and they must teach it that way as well. For schools, we help them to move away from their textbooks-as-curricula, and understand that nearly all available textbooks have incredibly great deficiencies, so great that only a very skilled teacher will be able to overcome them, We then help schools to address their standards and curricula to raise the difficulty and mathematical maturity slowing over those grades so students are prepared for algebra. For parents, we over free talks and pamphlets to help navigate what a good mathematics education would look like for their children.

One group I've not reached out to, even though I have many contacts in that group, is the homeschooling community. Should I? How? I'm happy to reach out to them as I do parents, but I haven't tried involving them as teachers.

My last institute was 5 full days. My next is going to be 9. It takes that many days just to begin to start to teach what mathematical reasoning looks like, even to experienced elementary math teachers.

I find that they homeschoolers I know are even less likely to find the time to attend such an event. One day workshops every month aren't enough. None of the homeschooling mothers I know, even if they are willing to afterschool Singapore, are willing to essentially take a course in learning elementary math if it required meeting weekly.

Am I pitching it wrong? Is there something I can do to reach them? I'm willing to admit that I must be all things to all people, but what would it take to get to them?

I already have to thread the needle--positioning MSMI as supporting teachers in a way that makes them not feel attacked for lacking content knowledge, but instead, supportive of their being asked to teach more and more sophisticated math. I have to reach administrators and tell them that their textbooks are terrible and teachers don't have the knowledge they need to do what their state has asked them to do, and they've basically been given no other options, since all US textbooks are terrible and elementary teacher certs don't require any math. I have to help parents to feel empowered even as I sound the alarm about their child's math program.

That's a lot of defensiveness to dance around. And yet, in homeschoolers, it seems even higher. So even as they admit to me that they don't know any math, and their children know more than they do, they don't want to learn more.

What should I do? How could I reach them? What would it look like?

onward and upward

party on

"University administrators are the equivalent of subprime mortgage brokers," he says, "selling you a story that you should go into debt massively, that it's not a consumption decision, it's an investment decision. Actually, no, it's a bad consumption decision. Most colleges are four-year parties."

Technology = Salvation