kitchen table math, the sequel

Mathew's in it!

And Ken is now officially a respected independent blogger! (scroll down)


trip down memory lane

First time any of us "met" Ken was September 27, 2005, when he left his famous Comment re: engineering school and engineering school wash-outs.

Tour de force

I finally found a good video that shows what differentiated instruction really looks like in a typical classroom, metaphorically speaking.



Who can come up with different examples?

NCLB is vague in its requirements with respect to measuring reading ability. NCLB is concerned with "proficiency in ... reading or language arts." That is the extent of the guidance given to us.

We know that reading is a complex skill comprising various subskills and content knowledge. But, what does it mean to be a proficient reader? What standardized test or battery of tests exist that accurately measure the "reading" ability of children and whether they are proficient?

Further, under NCLB it is the educators whose performance is being measured, even though the students are the ones taking the test. So the testing instrument must not allow educator subjectivity and must not be capable of being gamed by the educator. For example, Elizabeth's example in the post below describes a test that can be gamed by an educators since students can be taught to memorize the words appearing on the test and, thus, the test is not a true reflection of reading ability.

So, pretend you are a new superintendent of a school district who wants to accurately determine the reading ability of the children attending the schools in your district and how well they are being taught. So, for example, you want to know that your third graders are reading at a third grade level and will be capable of reading at a fourth grade level next year. You get to pick the standardized test(s) to be used. You will have non-reading-specialists monitoring the administration of the test(s). The monitors can identify outright cheating by teachers and/or students but nothing more subtle than that, i.e, they are incapable of making substantive determinations related to reading of any kind Otherwise, the administration of the tests is out of your control. Only the results of the test(s) will be reported to you.

What assessments do you select and why?

A presidential panel said yesterday that America's math education system was "broken," and it called on schools to ensure children from preschool to middle school master key skills.

...

F. Joseph Merlino, project director for the Math Science Partnership of Greater Philadelphia, which runs a research program involving 125 schools in 46 school districts, said that while he agreed with the finding that "you can't teach so many topics that you aren't able to get into depth," he disagreed with the report's focus on improving algebra instruction as central to better math education for all students.

He said he favored tailoring math instruction to the learning styles of students more than the report does. (emphasis added)

Philadelphia Inquirer, Panel: Math education is 'broken' The presidential panel called for ways to improve teaching and fight "math anxiety."

Bear in mind that in 2005, only 15.8% of black 11th graders in Philadelphia performed at the proficient level or above on the state math test. This placed them 2.61 standard deviations below the mean pass rate of 52.8% in Pennsylvania. This places these students below the first percentile.

See here.

I guess they haven't found the right learning style for these students yet.

The first time Wildenstein saw his newly-sculpted wife, he was said to have screamed in horror, unable to recognise her.

The horror.

From what I've seen so far, Everyday Math (EM) has few redeeming qualities as a primary source of elementary math instruction. I have heard that it works well as a supplemental source of instruction. I suppose the idea is 1. to use EM as a source of somewhat atypical practice problems and 2. that students will get more out of EM's conceptual oriented pedagogy if they have a firm prior understanding of the underlying procedures.

I remain somewhat dubious of the efficacy of both of these rationales. From my experience with the first and second grade EM materials, a large percentage of EM's practice problems are simplistic, dopey (that's a technical term), or both. Usually both. And, the amount of practice problems is woefully inadequate even for students who don't require as much practice (i.e., the students who typically excelled under the traditional curriculum). Moreover, EM's "conceptual understanding" is wildly overrated. Conceptual understanding does not begin and end with pattern matching as the authors of EM seem to think. A much better supplemental curriculum for teaching conceptual understanding is Singapore Math, but I digress.

Nonetheless, the best way to get through EM without befuddlement and tears is to treat EM as a supplemental curriculum. This implies that some other curriculum needs to be used as the primary curriculum. It also implies that the primary curriculum needs to stay ahead of the rather steep spiral employed in EM. This won't be easy because teaching to mastery takes longer that teaching to exposure which is how EM accomplishes its brisk pace and steep spiral.

Step One: Identify the Enemy. Beginning no later than kindergarten, you need to identify the math curriculum used in your school. If it is EM or some other fuzzy curriculum you need to select, secure and begin using a primary math curriculum in order to not only get a jump on first grade but to also take advantage of the light homework load of kindergarten and (hopefully) first grade.

Step Two: Select Your Weapon. I'm going to cut right to the chase here and tell you that my weapon of choice is Connecting Math Concepts (CMC). Other popular choices are Saxon and Singapore Math, but I picked CMC primarily because I thought it would minimize the amount of work I'd have to do. So far it has and I don't expect that to change. There are other reasons to select CMC:

1. It is fully scripted. This is key because while I fancy myself as an expert of elementary math, I am smart enough to know I am no expert in teaching elementary math. And, quite frankly, I don't want to become one. All I know is that when I try to teach a concept using my own words, I get a blank stare at least 50% of the time. When I use the script, I've never gotten a blank stare in over 200 lessons. You can't argue with that kind of success and I don't plan to.
2. The scripts are short. The teacher-led parts of each lesson take about 15 minutes to get through. The rest of the lesson involves the student working problems he's just learned or working distributed practice problems. I spend this part of the lesson in the teacher lounge, i.e., on my couch. I only emerge at the end to do a work check and to say "good job." Now, that's what I call teaching.
3. Zero prep time. My prep time consists of opening up the teacher's manual and doing some pre-reading as the student works some problems. I suppose if I was presenting to a class of lower-performers, I'd want to home my performance. But one non-low-performing student can tolerate an unpolished performance.
4. The scripts use simple language. Simple language is good because since you're going to be pre-teaching a student who is on the younger side of the expected student level.
5. Ample distributed practice. Distributed practice is built into the curriculum. This means you don't have to make-up your own practice sets. This means less work for you.
6. More is more. The curriculum is designed so that lower-performers can succeed. This means that your average or high performer will succeed as well. The only trick is to know when to cut back on practice problems, when to skip lessons, and when to convert teacher-led sections to independent work (this is a classroom curriculum in which some students will likely be absent, so teacher-led portions are repeated for absent students. My student, by definition, is never absent.) The general rule is that it is easier to cut than it is to supplement.
7. Relatively cheap. You can pick up used materials for about $100 from EBay. Textbooks and workbooks are easy to come by. Teacher presentation books not so much. The presentation books are the script. There is supplemental materials, but you can generally skip those unless the student needs extra practice, which is unlikely.
8. Aligns well with EM. Almost everything taught in EM has been covered in CMC, at least so far. Concepts that have not been covered are generally concepts that most consider outside or tangential to traditional elementary math anyway, so relying on EM to teach these concepts is largely inconsequential. These are inert concepts anyway, nothing builds on them and they are not important to future learning, so not learning them to mastery now isn't critical.
9. CMC is aligned with Math Mastery. Math mastery is a dvd/online review course for elementary math. It was designed to remediate struggling students, but that doesn't mean you can't use it for review or for teaching some topics for the first time. The lesson presentation is very similar to CMC, except that it's multimedia. Kids like that kind of stuff. Go check out a sample lesson. My son wanted me to teach him multi-digit division. That's a topic that doesn't get covered until CMC level D where it is spread out over the course of the year. he didn't want to wait that long, so I just put in the division mastery dvd and he was introduced to division problems. He needs a lot more practice before I'll claim that he's learned it. But it's a good start.

Step Three: Calibrate your weapon. I've done the hard work for you here. No later than midway through kindergarten begin level B and strive to finish one level every 12 months. That's about three lessons a week at most. Remember weekends are your friend. So is summer vacation. And winter/spring breaks. Just don't go too long between lessons since the student is likely to partially forget newly taught topics if they've lain dormant too long. Why cause more work for yourself? Plus, one of the reasons why you're not relying on EM as the primary curriculum is to avoid this deficiency in the first place.

At this point you may be asking: what happened to level A? You can skip level A if you've taught your child how to count to twenty and how to recognize and write numbers, i.e., the knowledge that most middle-class families send their children to school with. plus, for some reason level A is difficult to find second hand. Also, level B reviews much of level A for the first few lessons anyway.

Step Four: Fire. Right now my son is in second grade and we are just finishing up level C of CMC and we have really slacked off this year since he has quite the busy social calendar this year and the amount of homework he's getting has increased. Nonetheless, we are way ahead of the EM curve by quite a bit. He can typically complete his EM homework in about 5 minutes with minimal parental involvement or explanation. I never have to re-explain an EM lesson to him because he already understands the underlying concept. And, he scores well on his tests. In short, I don't have to worry about what he's learning in EM or whether EM is adequately preparing him for higher level math.

The only problems we have are primarily related to bookkeeping. He is fluent with his math facts and can do quite a bit of arithmetic mentally. As a result, he doesn't like to show his work for work he can do mentally, especially when "show his work" means drawing a 7 x 8 array of dots or any of the other superfluous crutches EM relies on to excuse itself from teaching to mastery.

This is not exactly a bad problem to have.

I would have preferred that his school teach him properly in the first place for the same reason that I don't like having to re-bake bread I've bought from a bakery (especailly an expensive bakery).

So if you find yourself in the same situation, this is one proactive way to survive Everyday Math. And, it surely is less painful than going the reactive route which I do not recommend. Motivation is a difficult thing to win back once you've lost it.

I have a lengthy four part post on positive reinforcement techniques and classroom management by KTM2 irregular Palisadesk over at d-ed reckoning that's too long to cross post here at KTM2.

It is the antidote for all the stories you read by teachers who claim that they can't motivate their students. It's not that students can't be motivated, it's that teachers have never been taught effective techniques.

Don't miss it.

In this very interesting post by Steve Sailer on James Flynn's (of Flynn Effect fame) on his new book, What is Intelligence? Beyond the Flynn Effect, I noticed something regarding the Flynn effect I never noticed before. Namely, that while IQ's have been on the rise, not all aspects of IQ have been rising at the same speed. The three slowest areas of improvement are for information, arithmetic, and vocabulary, and comprehension.

I don't think it's a coincidence that these four areas involve some aspect of academic content while the remaining faster growing areas generally do not.

According to Flynn, massive IQ increases are not seen in all types of cognitive functioning, just in a couple of areas, which explains why kids these days don't seem all that much smarter, except at programming their new gadgets. The Wechsler Intelligence Scale for Children (WISC) is one of the most popular IQ tests. Here are its ten subtests, ranked in order from smallest to largest IQ gain over 55 years:

WISC Subtest	IQ Gains in Points 1947-2002	Sample Question
Information	2	On what continent is Argentina?
Arithmetic	2	If a toy costs $6, how much do 7 cost?
Vocabulary	4	What does "debilitating" mean?
Comprehension	11	Why are streets usually numbered in order?
Picture Completion	12	Indicate the missing part from an incomplete picture.
Block Design	16	Use blocks to replicate a two-color design.
Object Assembly	17	Assemble puzzles depicting common objects.
Coding	18	Using a key, match symbols with shapes or numbers.
Picture Arrangement	22	Reorder a set of scrambled picture cards to tell a story.
Similarities	24	In what way are "dogs" and "rabbits" alike?

We see only small changes in the first three mental skills: general knowledge, arithmetic, and vocabulary. And
yet these are the skills that come up most in our casual conversation

However, there have been substantial improvements in the next six subtests, most of which involve visual logic. The proliferation of visual imagery was one of the major changes in the social environment in the 20th Century. People have much more practice at decoding images quickly than in the past.

Catherine here, diving into Ken's post.

This is the "fuzzy math makes you smarter" issue. All of those "find the pattern" constructivist math textbooks resemble the items on the Ravens Progressive matrices.

From the NYT:

Barbara R. Morgan got back to teaching yesterday. The students were in Idaho; she was in space, orbiting aboard the International Space Station.

...

The event yesterday was the culmination of a summer of space-related activities at the Discovery Center of Idaho, in Boise. Ms. Morgan, who is now what the space agency calls an educator astronaut, told the students that being an astronaut was not so different from being a teacher, at least in some ways.

“We explore, we discover and we share,” she said. And both “are absolutely wonderful jobs.”

What the hell is she talking about?

tour de force

From a response to Why Minimal Guidance During Instruction Does Not Work, which Ken discussed awhile back, one of the most pointed and useful statements of the constructivist take on content vs skills I've seen.

Useful as Exhibit A, I mean.

[M]y argument is that the concerns [with instructional effectiveness] of Kirschner et al.... are misplaced and that the most pressing concern facing educators and challenge to educational reformers is not in fact how to teach students but rather what to teach them. In other words, whether or not they have a correct answer, Kirschner et al. do not address the most pressing question.

WHAT DO WE WANT CHILDREN TO LEARN?

[snip]

Traditional answers to the question of what schools should teach children have become increasingly hard to justify. Beyond basic literacy and numeracy, [ed.: basic?] it has become next to impossible to predict what kinds of knowledge people will need to thrive in the mid-21st century. Like knowledge acquisition, another traditional goal—education for citizenship—is far from straightforward to characterize or implement. Examples across the world illustrate the dangers of ideological teaching that narrows students’ perspectives to the point of accepting only their own “right” way of understanding human affairs. [ed.: good point! let's forget the character ed & spend the time saved teaching the liberal arts]

A resolution has been in the direction of undertaking to teach not simply knowledge itself but the skills of knowledge acquisition—skills that will equip a new generation to learn what they need to know to adapt flexibly to continually changing and unpredictable circumstances (Anderson, Greeno, Reder, & Simon, 2000; Bereiter, 2002; Botstein, 1997; Kuhn, 2005; Noddings, 2006; Olson, 2003).

[snip]

After examining possible alternatives, I make the case that the only defensible answer to the question of what we want schools to accomplish is that they should teach students to use their minds well, in school and beyond (Kuhn, 2005). The two broad sets of skills I identify as best serving this purpose are the skills of inquiry and the skills of argument. [ed.: also remembering stuff] These skills are education for life, not simply for more school (Anderson et al., 2000). They are essential preparation to equip a new generation to address the problems of the day. [ed.: unless it turns out you have to remember stuff to address the problems of the day]

We have only a brief window of opportunity in children’s lives to gain (or lose) their trust that the things we ask them to do in school are worth doing. [ed.: like remembering stuff; remembering stuff is worth doing] Activities centered on inquiry and argument enable students to appreciate the power and utility of these skills as they practice them. [ed.: they're pulling your leg] They learn for themselves what they are good for, without having to be told, and become committed to them as tools for lifelong thinking and learning. [ed.: snort]

[snip]

Meanwhile, science educators have moved increasingly to the view that the most important thing children have to learn about science is to recognize science as a way of knowing the world, one that distinguishes it from other kinds of knowing and serves as a powerful tool for understanding (see Lehrer & Schauble, 2006, for review). [ed.: I guess you can pretty much accomplish that in a semester or two...]

[snip]

As for the claim that engaging in problem-solving produces cognitive overload, isn’t problem-solving, often unstructured, exactly what students need to become equipped to do? [ed.: you have to remember stuff to solve unstructured problems] Surely a steady diet of “worked examples” cannot possibly prepare today’s students for what they will face in the 21st-century world.

source:
Is Direct Instruction an Answer to the Right Question?
Deanna Kuhn
Teachers College
Columbia University

number one: Apparently these people have never met a middle-school aged child in person.

number two: The words parents, taxpayers, broader public, mathematicians, scientists, etc. do not appear in this article. That's too bad, because parents, taxpayers, the broader public, mathematicians, and scientists, etc. may have thoughts about what to teach America's children, possibly involving the importance of remembering stuff.

number three: The future, as imagined by constructivists, reminds me a bit of the old Future, the 1960s Future of Disneyland, G.E., and the Weekly Reader: spiffy, new, generic. In Professor Kuhn's 21st century, people will not have jobs or professions that require them to remember stuff. Jobs will be obsolete, and citizens will devote their lives to inquiring into and arguing about the issues of the day.

So I guess everyone will have a blog.


Center for Cognitive Technology
Education for Thinking Project

Ken De Rosa who is familiar to readers of KTM II and his own D-Ed Reckoning can be read in action now here as he takes on Nancy Creech, a whole language teacher from Oxford Michigan. For those looking for a fight on the order of Rocky Balboa vs Apollo Creed, this would not be the place in my opinion. Ken's arguments and command of facts makes it look more like Bill Clinton vs Lyndon Larouche. I'll let you figure out who's who.

from rightwingprof, one of the most succinct & clear statements I've seen:

Before I go on, let me quickly address why we must analyze the data statistically, and cannot just report means. If we gave the same kids the same proficiency exams on two different days, say only a week apart, their scores would be different. Anytime we see a difference between scores, without statistics, we do not know if those differences are due to random variation or not. We cannot without statistics point to two different scores or means and say, "See? The scores increased!"

Also, let me mention a few crucial points.

• The more data we have, the more reliable our statistical analysis will be (this will become an issue later on).
  

• Means (averages) alone do not give us a complete picture, particularly when they are means of aggregated data, as these are (this is why I look at other descriptive statistics).
  

• Statistics always deals with probability (uncertainty), and we calculate our statistics to a specific probability, 95% here (sometimes statistics are calculated to a 99% probability). This is the level of sensitivity (alpha), here, 0.05.
  

• We are assuming here either that the proficiency exam standards did not change between the two years or that the proficiency reports for the two years are comparable (if they are not, then Wisconsin cannot make any statement about their proficiency levels over time).