kitchen table math, the sequel: 2/14/10 - 2/21/10

Saturday, February 20, 2010

math wars

comment left on Numbers Wars: School Battles Heat Up Again in the Traditional versus Reform-Math Debate in the March issue of Scientific American:
Sad but true. I was at a fast food drive thru when the computers were down. They had to make change the old fashioned way. But the girl could not figure out how much change to give me. She seemed lost as she tried to calculate the difference between what I gave her and what the food cost. She had to call in the manger, who took way to long to compute the change (eventually she found a hand-held calculator).

Apparently even simple arithmetic is no longer well taught, learned and/or retained. Reliance on machines to "teach math" is only good if one has a machine when it is needed. My daughter had these classes where the calculator was required. The problem was that after smacking the keyboard a few times, she could come up with an obviously nonsensical answer. She would just write it down and move on. I asked her one time how she could multiple two numbers that each were less than one and come up with an answer that was greater than ten. The blank stare said it all (fyi - she failed to enter the decimal points correctly).

Want to terrify a teen-ager? Ask them to multiply 12 times 12. Is the answer immediate or not? Forget adding simple fractions. And we expect these kids to learn algebra and higher mathematics?

Are kids today less proficient even in arithmetic than in the past? Surely we can tell if these newer teaching methods are getting better results or not. As for me, I think my daughter did better in arithmetic in elementary school. After middle and high school, she seems to have "lost" the ability to easily do the arithmetic she learned earlier in life. I blame the calculator.
Twenty years of reform math.

That's a long time.

Thursday, February 18, 2010

rightwingprof: "I Would Like an Answer Now"

Clay Bond posted this to rightwingprof on March 29, 2006. It's a keeper.

'Yes, I posted this some time ago. However, the questions are not rhetorical. I really would like an answer from my colleagues in the primary and secondary school system — particularly those in the education union establishment. And I’d like an answer because I really do want to know why I have to do your job as well as mine.

Thanks ahead of time for your response. Here it is:

I don’t want anyone to get the wrong idea. I’ve had many extremely bright students. Many. Some had the necessary knowledge for the class, and some did not; of those who did not, most worked their butts off and did well. I also don’t want you to think smarts are what I care most about.

My favorite students are the ones who aren’t that bright, but work their tails off to do as well as they can. My least favorite students are the ones who are extremely sharp, but don’t work.

Sometimes, however, there’s too much missing knowledge, so much that the best thing the student can do is drop the class. It breaks my heart when I get a student like this.

I had a student some time back I’ll call Mark. Mark was bright, though his high school had cheated him, and he was lost almost from the first day. He worked hard, and came to my office hours. But … well, there was too much missing, as I discovered early in the semester when he was in my office.

I asked him what he wanted me to clarify, and he said he didn’t understand the 68-95-99 Rule. The conversation went something like this:

Me: “In a normal distribution, 68% of the data fall within one standard deviation in either direction of the mean. So here’s our distribution,” I drew a bell curve on the whiteboard, “And here’s our mean,” I drew a dashed line bisecting the curve. “Our mean is 50, and our standard deviation is 2, so 68% of the data fall between 50-2 and 50+2, 48 and 52.” I drew lines and arrows, and a 68% beneath.

Mark: “I don’t understand. Wouldn’t it be 75?”

Me: “Wouldn’t what be 75?”

Mark: “The mean.”

Me: “Why would it be 75?”

Mark: “That’s what you said in class.”

Ah. He was stuck on the example — and being a firm believer in introducing concepts in contexts familiar to students, I introduce basic descriptive stats in terms of grades, since what else are students more familiar with?

Me: “The mean could be 75, sure. In this particular distribution,” I pointed to the curve on the whiteboard, “the mean is 50.” I then erased the 50. “But let’s say the mean is 75,” and I wrote 75 after the x-bar, “then 68% of the data falls between 75-2 and 75+2, 73 and 77.”

Mark: “How do you know if the mean is 50 or 75?”

One of the difficult parts of teaching is diagnosing the problem. Students have questions, but the problem may actually be more fundamental than what they are asking about, as I was beginning to understand here.

Mark was having two basic problems: He didn’t understand what a mean was, and he was having trouble abstracting the idea out of the example. The former is easy to fix; the latter is not.

Me: “Can I erase this?” I pointed to the whiteboard, and he nodded. I erased the curve, and wrote a series of numbers on the board in a vertical column: 90, 85, 70, 65, and 50. “These are test scores,” I said, “How do you calcualate the mean, or average?”

Mark didn’t volunteer an answer.

Me: “Okay, let’s say the whole class takes an exam, and these are the scores. An average, or mean, tells me how well the class did overall. To calculate the average, I add all the scores, then divide by the number of scores. Here, you do it.” I have him the marker.

Mark added the numbers, then stopped.

Me: “How many scores are there?”

Mark: “Five.”

Me: “Okay, divide the total by five.”

Mark complied.

Me: “What’s the mean?”

Mark: “Seventy-two.” He looked at the numbers for a minute, then smiled. “I get it!” he said.

That’s when I realized what I’d suspected: Mark was a university freshman who had not, until just now, understood the concept of an average. I found that disturbing, but Mark was on a roll.

Mark: “So what’s a median?”

Me: “The middle score.” I pointed to the five numbers. “Half of the scores will fall above the median, and half will fall below the median. What’s the median of these scores?”

Mark: “Seventy.”

Mark was in my office three hours. No wonder he’d been lost. He didn’t understand an average. He didn’t understand sampling or distributions. We didn’t get to the 68-95-99 rule that day, because there was too much he didn’t understand.

I worked with him twice every week, and he got a B in the class. He worked harder than nearly any other student I’ve had. But if he had not come to my office every chance he got, he would never have passed.

Mark had no sense of entitlement. He wanted to understand, and he wanted a good grade, and he worked for both. He was bright. The thing is, I pretty much ran him through a high school math program in the office during the course of the semester.

I’m a teacher, so I can ask the obvious question, and some other teacher can’t come back with any of the usual non-answers.

I did it. Why couldn’t you, when Mark was in high school? It’s not money. I got no extra pay for helping Mark. It’s not time. I spent many hours in the office working with him. It’s not his intelligence or ability to learn. He’s smart, and he learned quickly, once we got started.

So I’ll ask again: Why couldn’t you do your job? It wasn’t my job to teach Mark high school math, but I did. Why did I have to? How did Mark get through all the required high school math courses without understanding what an average is? How did Mark get through all the required math courses without ever having seen y=mx+b? How did Mark get through all the required math courses and not understand that each flip of the coin is independent of all others? Most of all, how did you, his teachers, let such a bright, hard-working, motivated student slip through the cracks?

What’s going on there?

rightwingprof at ktm


speaking of rightwingprof

I've just seen this posted on the Clay Bond Memorial Facebook Page:
warning to Clay's Internet friends: Central Pennsylvania Orthodox will probably stay up for awhile because it runs on freeware. Right Wing Nation will vaporize at some point because there is a monthly charge for the blogspace. Cut and scrape things you want to keep, ok?
I'm going to save I Want an Answer now, but there must be a zillion other keepers on his site--does anyone have any ideas?

why can't U teach me to read?

Years ago, I asked a special needs attorney when it would be possible for parents of general education students to sue schools. He wasn't encouraging. (scroll down) In fact, he wasn't even interested.

I had thought such a case finally existed, but now that I've looked at Jennie's links (thank you, Jennie!) I see we're not there yet.

That's fine. I'm patient.

I miss rightwingprof.

Why can't U teach me 2 read?: Three Students and a Mayor Put Our Schools to the Test by Beth Fertig
due process for parents of general education students
diagnosis diagnosed
crack in the wall (educational malpractice)
status quo la-la-la

Wednesday, February 17, 2010

Laurie Rogers on the Delphi Technique

I remember, back when I started writing ktm-1, somebody mentioning the Delphi technique. At the time, I thought: that's a little far-out.

Now I think: what a helpful explanation!

My own district has been using a variant of the Delphi technique in its Budget Forums, but we seem to be past that now. I'm told that, at the last forum, someone stood up and suggested that employees take a pay cut in order to prevent further tax increases and the room burst into applause.

Laurie Rogers on the decision

I would like to think if we stuck central office administrators in a reform math classroom and forced them to endure the torture they call K-12 math instruction, they would come to see the light, but I fear they would just get out their color-coded sticky notes, their pens and highlighters and happily spend the rest of the day muddling in herds, getting nowhere, certain that their talking, scribbling and checking for group consensus means "real learning" is going on.

Very droll.

I like droll.


Barry on the Seattle decision

Barry clarifies the question of whether the court ordered the Seattle school district to adopt a particular curriculum (which is what I assumed when I read the news):
....the court did not rule on the textbook or curriculum. Rather, it ruled on the school board’s process of decision making—more accurately, the lack thereof. The court ordered the school board to revisit the decision. Judge Julie Spector found that the school board ignored key evidence—like the declaration from the state’s Board of Education that the discovery math series under consideration was “mathematically unsound”, the state Office of the Superintendent of Public Instruction not recommending the curriculum and last but not least, information given to the board by citizens in public testimony.

The decision is an important one because it highlights what parents have known for a long time: School boards generally do what they want to do, evidence be damned. Discovery-type math programs are adopted despite parent protests, despite evidence of experts and—-judging by the case in Seattle—-despite findings from the State Board of Education and the Superintendent of Public Instruction.
Skydiving without Parachutes
Ed says he heard on NPR of a successful court case in which a parent successfully sued a district for failing to teach her child to read -- apparently someone has written a book about the story.

Has anyone heard anything about this?

Singapore Math at Hackley


One question: I don't remember a lot of focus on manipulatives in Singapore Math -- ?

How do Singapore schools handle struggling students?

Hackley School

momof4 on college planning

momof4 says...

I have always felt that the preparation for high school is too little and too late, both in terms of academics and of advance planning. Especially in a system where APs have prerequisites, kids and parents need to know that so they can plan coursework accordingly.

All of the schools my kids attended waited until 8th grade - usually spring -to address the HS plan. Parents need to know the critical nature of the usual sixth grade test, which determines who gets on the top math path, which will also determine eligibility for AP Physics BC (calculus is a co-requisite). There is just far too much mush and wasted time; kids without aware parents who are able to supplement are hosed before they hit 7th grade.

BTW, I've found it fairly common for a shared MS-HS campus, so taking some classes at the HS may be possible. Also community colleges, universitites etc - whatever is available.

SAT scores predict grades in individual courses

contra FairTest....

Individual Differences in Course Choice Result in Underestimation of the Validity of College Admissions Systems
by Christopher M. Berry1 and Paul R. Sackett2

ABSTRACT—We demonstrate that the validity of SAT scores and high school grade point averages (GPAs) as predictors of academic performance has been underestimated because of previous studies’ reliance on flawed performance indicators (i.e., college GPA) that are contaminated by the effects of individual differences in course choice. We controlled for this contamination by predicting individual course grades, instead of GPAs, in a data set containing more than 5 million college grades for 167,816 students. Percentage of variance accounted for by SAT scores and high school GPAs was 30 to 40% lower when the criteria were freshman and cumulative GPAs than when the criteria were individual course grades. SAT scores and high school GPAs together accounted for between 44 and 62% of the variance in college grades. This study provides new estimates of the criterion-related validity of SAT scores and high school GPAs, and highlights the care that must be taken in choosing appropriate criteria in validity studies.
Psychological Science
Volume 20—Number 7

Thus, to the degree that prediction of grades is a goal of college admissions systems, SAT scores and high school GPA are clearly useful tools for deciding which college applicants will achieve the greatest levels of academic performance.

Inside the same class, the student with higher SAT scores/h.s. grades does better than the student with lower SAT scores/h.s. grades. High school grades were a slightly stronger predictor than SATs.

palisadesk on Direct Instruction and Whole Brain Teaching

(Part 1) Coming back to Liz's question at the end of her post, How congruent is [Whole Brain Teaching] with Direct Instruction, I would have to answer: Not.

The WBT people have adapted some ideas from DI and other sources (Peer-Assisted Learning, Kagan's Cooperative Learning, Fred Jones' Positive Classroom Instruction, Precision Teaching and still more). However, they have put their own spin on all of these so their variants differ in essence as well as in details from the originals.

Take unison responding -- something that is a prominent feature of DI programs at all levels. It is never used in DI as a "management" tool, nor as a rah-rah way to "pump up" the kids or manipulate them. The script, with its unison responses, is carefully researched to ensure clear presentation -- the exact wording, examples and non-examples to ensure than 95% of students will grasp the concept or skill being taught the first time, with practice to mastery built in over a spaced continuum of lessons. Unison responses are an empirically validated way of ensuring participation of all students, instant feedback to the teacher as to hope well the students understand or remember the presentation (if there are errors it is the teacher's responsibility to loop back and re-teach an item until all students can respond correctly. Individuals who make an error are not singled out, but are monitored closely and if additional practice is required for one or two, that is arranged separately so that the dignity of the student is always preserved.)

This I found an important distinction between true DI and WBT -- Engelmann (in his writings, his presentations, and his videoed interactions with children in all settings) is extremely respectful of the dignity of the learner. While he can be funny and show a humorous side (mostly at his own expense), I cannot imagine him ever presenting a task to students and then (as in the 4th grade critical thinking video) asking them to "beg me to let you do it." Even if in jest or in a good-hearted spirit, I found asking students to plead and beg en masse to be disturbing and degrading, however well-intentioned. The kids seemed to go along with it, which is even more disturbing. Why should children have to beg their teacher to engage in a valuable learning activity?

Another fundamental difference between DI and WBT is the principle of parsimony. Engelmann is very explicit in emphasizing the need for instruction to be parsimonious--- to contain nothing extraneous, to include the minimum verbiage needed for clear communication, to require only the amount of practice needed to mastery -- no more and no less. Extraneous yakkety-yak, whether by teacher or students, is a no-go.

It would be completely alien to DI to have the teacher explain a new concept to the class, then ask the STUDENTS to explain it to each other. It's the teacher's responsibility to ensure the students grasp it, not the responsibility of the student's partner. All the scripted cheers and call-and-response stuff in WBT is totally foreign to the DI principle of parsimony, and to the concept of respect for the learner as well.

Only the instructional language in DI is scripted; the teacher is trained to give lots of positive feedback (at a ratio of 5:1 or better), and to teach in an animated and engaging manner, but how he or she does so is an individual matter. This means the teacher can adapt praise and encouragement to his/her own style and the culture of the community or classroom.

Also, DI has the scripted unison-response component to every lessons, but that is only a part of the lesson. All lessons also include individual work, sometimes partner work, sometimes small-group work, so children are not being overwhelmed by all the noise and demands to produce a response. DI makes tracking points an optional feature, but does not suggest extrinsic rewards for these (it suggests they could be tied into normal student evaluation), although teachers may use them in this way if they feel it is necessary, as is sometimes the case.

Finally, DI fundamentally differs from the example of WBT that I saw in several videos, in that it regularly monitors progress in an empirical manner so that the teacher knows what every child is learning, and ensures mastery through a research-based set of criteria at multiple points.

Although the program itself is very tightly crafted and leaves no room for "creativity," the teacher's creativity can blossom in its application and in response to the needs of the individual learners as the program moves along. In fact, it frees the teacher to be more attentive to kids' responses and to devise ways to help them overcome whatever hurdles present in their path. Not needing to re-invent the wheel in every lesson, the teacher can truly engage with and pay attention to each individual student s/he teaches.

(part 3) To be fair to WBT, some of the videoed activities I saw were pretty well done and are based on sound precedents. The one on the Speed Read 100 or something was a good example of peer-assisted learning under a teacher's direction, with children encouraged to help each other (within a pre-trained format), to aspire to beating their own record and to celebrate small steps forward.

If it weren't for the other accoutrements, I would have given this activity two thumbs up, but it was pretty good. I would recommend Peer-Assisted Learning Strategies (see Sopris West for some examples for the primary classroom) as it has a positive effect in several areas, including achievement, student motivation, building classroom community, student self-confidence, and so forth. Similarly, some of the Kagan strategies, such as Think-Pair-Share and Turn and Talk are also well-validated empirically but do not need to be carried out in the chaotic manner we saw in the videos.

Another point: attention signals, such as Class-Yes! are a valuable tool in any classroom. What bothered me was not that they used it, but how it was used -- in a theatrical, almost buffoonish, hyperdramatic way. Learning can be fun and engaging, but it shouldn't be a joke, a circus or a day at the football stadium.

For primary kids, a good attention signal is (teacher says, in calm rhythmic voice) "1,2,3, eyes on me!" Children stop where they are, turn and face the teacher and clap. "1,2, eyes on you!" This is used in a purposeful manner, when something needs to be said to the whole group but it is not necessary for everyone to go back to their seat as if for a lesson. There's nothing manipulative about it, either. Class-Yes! in a straightforward way would be fine for older students, I think. I myself would not allow yelling and silliness to accompany it. We want to keep the focus on learning.

To that end, gestures can be very useful. A popular and effective program for K in the UK, Jolly Phonics, uses hand signals (called "actions") to teach the letter-sound correspondences. I can imagine similar applications at other levels. These have at least two positive benefits: they give the wiggly, energetic student an opportunity to engage in a physically active way, and they provide the teacher with instant formative assessment data on how well the lesson is progressing.

.....I doubt there are any videos out there that show DI and WBT and contrast the differences. WBT is a recent development and that explains why ... there isn't any longitudinal data on how effective it is in ensuring student learning. As for videos exhibiting DI, most that I have seen consist exclusively of video of the teacher presentation (the scripted part) since that is the most difficult to learn to do well. Signaling, pacing and knowing when to loop back and review are the hardest elements to master....

Since basic differences between the two lie in underlying philosophy and curriculum design, those wouldn't be apparent anyway. However, I did note that none of the WBT videos I saw consisted of a teacher presentation that appeared "scripted," i.e. specific language from the teacher, requiring a specific instruction-related response from students, over a period of several minutes. The "scripting" in the WBT videos consisted of management call-and-response practices, not scripted presentation of concepts and content.

Also, I don't know of any DI videos that include the whole lesson -- the non-teacher-directed parts. They don't depict the independent work period, student partner work, or small group/team work. These are an essential element of every lesson, as is the "work check:" students and teacher review and correct the independent work at the end of the lesson, to ensure students can clarify any misunderstanding before going on to the next step.

As for preschool, DI does offer specific programs for that level, most notably in language skills and verbal reasoning. They don't recommend moving on to reading instruction until children are proficient in the language skills, which include making comparisons, understanding and using if/then statements, applying a rule (if all birds have feathers, and Paco is a bird, what else do we know about Paco?).

(2 of 2) The early phases of the reading program for this level teach a lot of the phonological processing skills (blending and segmenting sounds, sequencing,left-right progression) needed for successful reading later on, and introduce only very regular grapheme/phoneme correspondences, in a special orthography modified to be less confusing to very young children whose visual perception and visual efficiency skills are less well-developed.

The letters are darker, bigger and "fatter," with distinct differences between the u and n, the p and q, the b and d, so as to prevent children's confusing them. Visually similar letters are not taught together, but presented one at a time, and when one of the pair is introduced, it is taught to mastery before the other is introduced. The program for 4-year-olds moves quite slowly, and many elements are taught in a playful or gamelike way, with lessons expected to take only about 15 minutes. So it is unlikely a child would be "unready" (after completing the language sequence), and s/he would not be pressured to move too fast.

There is very little written component at this stage; the seatwork consists often of coloring, tracing or making discriminations, such as crossing out an item that doesn't belong. These provide short, frequent opportunities to develop graphomotor skills, but not to the point of frustration.

DI is most valuable at the preschool level for children with a less-advantaged language background, though in Engelmann's early work his comparison group of "middle class" kids took off like a rocket with DI and were able to do very advanced work in reading and math by age 6, as well as verbal reasoning skills that Piaget thought impossible before age 11 or 12. He talks about that in one of his books; I'll see about finding an appropriate link....

remembering what you understand

Reading through the whole-brain thread I've just come across this observation by Tracy W:
Understanding is good, but it's only momentary. In my work I often spend hours trying to understand a problem, and then finally getting the flash of insight. And I've learnt that when the flash of insight comes I need to write it down and store it somewhere I can find it again, because otherwise I forget.
There's a terrific scene in Mad Men built on this premise. One of the copy writers stays up all night working on a brilliant idea for an ad campaign, and then, the next morning, he can't remember what his brilliant idea was.

The punchline: with Don Draper glowering and Peggy Olsen nervously trying to cover for her colleague, the guy finally cracks and says, "I had a brilliant idea, but I don't remember it."

There's a beat while the audience waits for Don to blow up.

Then Don says, "I hate when that happens."

Monday, February 15, 2010

College Application & Class Rank

I know that GPA (class rank) is one of the key factors in college applications, but applications have to be sent in before much of anything is known about the senior year. Does this mean that the courses you take in the senior year and grades you get don't matter so much? I know that colleges check to see if you crash in the senior year, but exactly what do they know about the senior year? Does this mean that the class ranking at the end of the junior year is all that the college knows? If so, does this mean that students should try to get more AP classes in before the senior year?

I was also looking at the course catalog for the high school my son will enter next year. It finally (!) struck me that if he wanted to take an AP science course, it has to come after taking the regular honors version. Is this typical? Do some kids get authorization to go directly to the AP version? This relates to the senior year issue. If colleges can't base their decisions on the results of the senior year, then do some kids relax their schedules a little in the senior year - perhaps not cram in every last AP class they can?