kitchen table math, the sequel: practice
Showing posts with label practice. Show all posts
Showing posts with label practice. Show all posts

Sunday, January 31, 2016

Most emailed

I have no doubt Adam Grant's op-ed on raising a creative child, which ran in yesterday's Times, is being emailed to teachers across the land:
Child prodigies rarely become adult geniuses who change the world....

What holds them back is that they don’t learn to be original. They strive to earn the approval of their parents and the admiration of their teachers. But as they perform in Carnegie Hall and become chess champions, something unexpected happens: Practice makes perfect, but it doesn’t make new.

[snip]

In adulthood, many prodigies become experts in their fields and leaders in their organizations. Yet “only a fraction of gifted children eventually become revolutionary adult creators,” laments the psychologist Ellen Winner. “Those who do must make a painful transition” to an adult who “ultimately remakes a domain.”

Most prodigies never make that leap. They apply their extraordinary abilities by shining in their jobs without making waves. They become doctors who heal their patients without fighting to fix the broken medical system or lawyers who defend clients on unfair charges but do not try to transform the laws themselves.

So what does it take to raise a creative child? One study compared the families of children who were rated among the most creative 5 percent in their school system with those who were not unusually creative. The parents of ordinary children had an average of six rules, like specific schedules for homework and bedtime. Parents of highly creative children had an average of fewer than one rule.

[snip]

SINCE Malcolm Gladwell popularized the “10,000-hour rule” suggesting that success depends on the time we spend in deliberate practice, debate has raged about how the hours necessary to become an expert vary by field and person. In arguing about that, we’ve overlooked two questions that matter just as much.

First, can’t practice itself blind us to ways to improve our area of study? Research reveals that the more we practice, the more we become entrenched — trapped in familiar ways of thinking. Expert bridge players struggled more than novices to adapt when the rules were changed; expert accountants were worse than novices at applying a new tax law.

[snip]

Hear that, Tiger Moms and Lombardi Dads? You can’t program a child to become creative. Try to engineer a certain kind of success, and the best you’ll get is an ambitious robot. If you want your children to bring original ideas into the world, you need to let them pursue their passions, not yours.

How to Raise a Creative Child. Step One: Back Off by Adam Grant | 1/31/2016
Creativity good, practice bad.

Oh, man.

Setting aside the mischief this is going to do, how many "adult geniuses who change the world" do we actually need?

And how often does a lone genius change the world?

Should all expert physicians "fight to fix a broken medical system"?

Should all expert attorneys "try to transform the laws themselves"? (All of the laws?)

As to the rigidity of experts, which is a real phenomenon, the solution isn't to get rid of experts.

Tuesday, October 13, 2015

Saving the hard stuff for home

Auntie Anne writes:
This has been our experience as well. Teachers are always trying to make "learning fun!", which means no boring stuff like worksheets and drills, but lots of group chatting/working, lots of craft work, lots of "exploration" in the classroom.

Still, the hard stuff has to happen, so they just send it home at night. Instead of school being where kids work, and home being where they can play and relax, the opposite is now true.

Meanwhile, the people who have the burden of getting kids through the not-fun part of their education end up being the parents who have to get their kids to get their homework done.
That's what suddenly hit me, the other day, talking to the mother of a second grade child who is melting down over her homework.

What is her child doing during the day?

I also realized that one aspect of Morningside Academy I haven't stressed is the fact that students there don't do homework.

Interestingly, I don't recall Kent Johnson telling us that Morningside kids don't do homework. I found out later, when I visited a precision teaching school in CT, where the kids did lots of homework. The principal told me that Kent's philosophy was that Morningside students worked hard during the day and should be free to play after school. She may have been wrong, of course, but in fact I don't think I saw children take homework home during the two weeks I attended the Summer Institute.

I definitely didn't see teachers collect homework.

So think about that.

Morningside teaches children in grades K through 8.

It guarantees that each students will make two years' progress in one year's time, in their subject of greatest difficulty, or tuition will be refunded. Most or all students are there because they're having difficulty in their regular schools.

And they make two years of progress in just one year without doing homework.

I know I've told this story before, but by the time we finally pulled C. out of our schools here, I had recurring images of the school scooping up heaping armloads of his childhood and tossing them in the trash.

(Does anyone remember Carolyn J. setting up the "FWOT" category on the old ktm? I sure do. Had never encountered the acronym before.)

More from Anonymous:
Yup. This was our experience as well. Soft, touchy feely classroom activities, and the hard stuff came home. Not only did it come home, it came home with a child who hadn't received any instruction about how to do whatever it was (and this was middle school).

Why can't they get it all done in the 6-7 hours the kids are in school? There should be no homework in K-8. Frankly, I don't think there should be homework in high school either unless they go over to a university model and drastically reduce the amount of time in class. K-8ers need time to be kids, and high school students need time to learn who they are beyond their schoolwork.
And chemprof:
The whole idea of homework with kids this age does mean that you are asking them to do the most intense academic work when they are totally wiped out.

That said, by second grade she needs to know her addition and subtraction facts (and if she doesn't, that's something they should be working on at home). They are starting to do multi-digit addition and subtraction, and that's tough without knowing the facts. That's where we are right now (2A Singapore Math), and without those math facts, we'd have lots of tears.

Since we are homeschooling, we do a lot of our heavy work in the morning or early afternoon. Sometimes we do work in the evenings, but only if she's in the mood. But we are also working on a checklist, so she's got a lot of control over what she does on a given day.

This is a great example of how FedUpMom says our educational system is neither traditional or progressive, but the worst of both. A real traditional system would have them doing the hard work all day, with a little homework to reinforce it at night. In a real progressive system, students would do projects and group work all day in school, with a lot more choice of activity, but then not have homework. Instead, they do the projects but follow up with homework that they aren't prepared to do.
And--ding! ding! ding!--lgm's district takes the cake yet again:
Well, the hard stuff didnt come home here. The tears come during prep for the state math test...when the district tries to cram the top kids into earning a 3. Most of the year is spent in remediation to benefit the included and poverty. The parent of the lad needs to afterschool like everyone else that is serious.
My conclusion: things have gotten worse.

C. didn't have lots of onerous homework to do--and I did start taking his math homework away from him & doing it myself at one point, as education realist advises.

Taking homework away from a conscientious child, by the way, is easier said than done. I took C's math homework away because I was trying to accelerate him so he could take algebra in 8th grade, which meant that he needed to do math practice well ahead of the homework being sent home. But C., only in 5th grade at that point, absolutely could not stand the idea that we were lying to the teacher and doing things wrong. So I didn't do it often.

Anyway, C. didn't have lots of onerous homework, so our time was taken up with reteaching, as opposed to reteaching and beaucoup homework, which may be where things stand today.

Saturday, October 10, 2015

Help desk - math HW

What's the story with this little boy's homework? (And how old do you think he is? I'm guessing 2nd grade - ?)

If you click on the link, you'll see a photo of a little guy crying, presumably about his math homework. The worksheet is titled "Using Mental Math to Add" or "Doing Mental Math to Add."

This photo was posted. Watch what happened next.

Assuming he's crying over the worksheet (I have no reason to think he's not) -- what's the problem?

By this point, would he know his addition facts?

Or is he having to do these problems without knowing his facts by heart?

Is there something else going on?

One thing I've become concerned by of late: children spending their days engaged in mini lessons and peer discussion, then doing the 'hard stuff' at home, when they're tired.

I was talking to the mother of a second grade child here who has some sensory issues. The little girl is getting completely overwhelmed at night, trying to do her homework. She melts down and sobs unless her other is in the room with her. Even with her mother by her side, she struggles to get through the work.

I asked how much homework she's doing, and it sounded like a lot. Too much. In math alone, she has a full worksheet to do and several minutes of computer practice.

Listening to the mom, I suddenly realized: it's entirely possible students here are doing no worksheets during class time at all.

The kids have to do worksheets because Common Core, but worksheets aren't constructivist and we are now a Tony Wagner district so .... maybe all the worksheets have to happen at home. Out of sight, out of mind.

But that means kids go through a full day of school and a full raft of after school activities before they start the real work.

Wednesday, December 11, 2013

In the world of MOOCs, 2 + 2 is never 4

The statistical model found that measures of student effort trump all other variables tested for their relationships to student success, including demographic descriptions of the students, course subject matter and student use of support services. The clearest predictor of passing a course is the number of problem sets a student submitted. The relationship between completion of problem sets and success is not linear; rather the positive effect increases dramatically after a certain baseline of effort has been made. Video Time, another measure of effort, was also found to have a strong positive relationship with passing, particularly for Stat 95 students. The report graphs these and other relationships between variables examined by the logistic-regression models and pass/fail.

While the regression analysis did not find a positive relationship between use of online support and positive outcomes, this should not be interpreted to mean that online support cannot increase student engagement and success. As students, Udacity service providers and faculty members explained, several factors complicated students’ ability to fully use the support services, including their limited online experience, their lack of awareness that these services were available and the difficulties they experienced interacting with some aspects of the online platform. It is thus the advice of the research team that additional investigations be conducted into the role that online and other support can play in the delivery of AOLE courses once the initial technical and other complications have been addressed.

Conclusion: The low pass rates in all courses should be considered in light of the fact that the project specifically targeted at-risk populations, including students who had failed Math 6L before Spring 2013 and groups demonstrated by other research to be less likely to succeed in an online environment. Previous studies (see Section 1) have found that these students do less well in online than in face-to-face courses. Further, student groups in at least one major study (Jaggars and Xu, 2013) who were found to experience the greatest negative effect from taking courses online share many of the characteristics found among the AOLE partner high school students in particular, a group with very low pass rates in Spring 2013.

Overall, much was learned during and from the first iteration of AOLE and improvements are already in progress in the second AOLE iteration. Perhaps most importantly, the faculty members who taught these courses, although they had to contend with major difficulties along the way, believe that the content that has been developed has tremendous potential to advance students’ critical thinking and problem solving abilities. One faculty member summed it up this way: "Udacity has brought to the table ways to make the courses more inquiry-based and added real life context."
PRELIMINARY SUMMARY SJSU+ AUGMENTED ONLINE LEARNING ENVIRONMENT PILOT PROJECT September 2013
Let's reprise.
  • The clearest predictor of success in the course was the number of problem sets students completed. In other words, practice. 
  • The online mentors, aka teachers-slash-tutors, didn't help. But they might have helped if students had a) had lots of internet experience (practice) & thus could figure out how to get to the mentors; b) known the online mentors existed; and c) been able to get the MOOC site to work.
  • "Previous research" had found that weak students do better in face-to-face courses, so….SJSU opted to run a MOOC and fill it with weak students.
  • "Most importantly," the teachers who taught the MOOCs think the "content" has "tremendous potential to advance students’ critical thinking and problem solving abilities."
Practice is what matters, so the instructors are focused on inquiry; weak students do badly in online courses, so the MOOC people put weak students in online courses; educational technology never works.

A person who lives in the world where two plus two equals four would be doing something else.

Eureka
Eureka, part 2
Eureka, part 3
Eureka, part 4
Eureka, part 5

Flipping the Classroom: Hot, Hot, Hot
MOOCs grow the gap
The New York Times is surprised
In the world of MOOCs, 2+2 is never 4
World's funniest joke: humor depends on surprise
Dick Van Dyke on comedy
Philip Keller on the flipped classroom
If students could talk
Who wants flipped classrooms? (Salman Khan on liberating teachers)
True story
Are math & science lectures boring in a way humanities & social science lectures are not?

Tuesday, July 30, 2013

Naturals and strivers


To understand how talent and achievement are perceived, three experiments compared the assessments of “naturals” and “strivers." Professional musicians learned about two pianists, equal in achievement but who varied in the source of achievement: the “natural” with early evidence of high innate ability, versus the “striver” with early evidence of high motivation and perseverance (Experiment 1). Although musicians reported the strong belief that strivers will achieve over naturals, their preferences and beliefs showed the reverse pattern: they judged the natural performer to be more talented, more likely to succeed, and more hirable than the striver. In Experiment 2, this “naturalness bias” was observed again in experts but not in nonexperts, and replicated in a between-subjects design in Experiment 3. Together, these experiments show a bias favoring naturals over strivers even when the achievement is equal, and a dissociation between stated beliefs about achievement and actual choices in expert decision-makers.

Naturals and strivers: Preferences and beliefs about sources of achievement
Chia-Jung Tsay, Mahzarin R. Banaji Journal of Experimental Social Psychology 47 (2011) 460–465
I wonder why this is?

Why would experts hold the bias (while believing they hold the opposite bias) while nonexperts don't?

Is this likely to be specific to the music world? (I have no idea.)

Friday, July 19, 2013

Doug Lemov has a new book out

Practice Perfect: 42 Rules for Getting Better at Getting Better

For several years now, when I think of the public schools, the first issue that springs to mind is the stark absence of any mention or consideration of the need for practice. In the 14 years we've had kids in our local schools, I don't believe I've ever heard an administrator use the word 'practice' in any context other than 'football practice' or 'basketball practice,' etc.

When the subject is academics, the word is always 'understand.' Students will 'understand.' Not practice.

That's a problem because although class time is all about understanding, the tests are about remembering: students are tested on what they know. Which means students have to practice the content taught in the classes, but the school doesn't worry about providing effective practice. Teachers give homework, but no one collects or corrects the homework, and no one asks whether the homework actually works. Does the assigned homework increase knowledge? Nobody knows, and nobody asks. Practice is not a topic of conversation. At least not within my hearing.

Naturally under this system (Teach, test, and hope for the best), parents end up hiring a lot of tutors --- but tutors can't really provide effective practice regimens, either. (Even if a tutor would like to provide a practice regimen, parents don't need a whole new set of homework-from-thetutor to deal with.)

So the core requirement of all learning -- practice -- is left to the kids.

Let's just hope they're following the literature.

Saturday, July 16, 2011

practice in school

Hey everyone - I'm back from IL (didn't get to see Susan S - darn!) - and have just read a brilliant comment left by Lynne Dilligent on Joanne Jacobs' blog. Lynne's comment sums up a core frustration I've felt with the schools forever, re: the need for the school, not the parents, to be in charge of providing and overseeing the practice children need to learn what they're supposed to be learning.

Must go do "SAT work" with C. -- back in a little bit.

(Thanks to Barry for sending the link.)

Wednesday, August 25, 2010

spaced repetition

Because I remained in the third form [grade] three times as long as anyone else, I had three times as much of sentence analysis, learned it thoroughly, and thus got into my bones the structure of the English sentence. The essential structure of the ordinary English sentence is a noble thing.

Winston Churchill
quoted in Sentence Composing for College

spaced repetition
spaced repetition and the chorus effect

Thursday, March 18, 2010

cumulative practice

I've been meaning to get a post up about this article for years now. I think it's incredibly important (relates to Direct Instruction, too).

No time to write now, but here's the abstract:

THE EFFECTS OF CUMULATIVE PRACTICE ON MATHEMATICS PROBLEM SOLVING (pdf file)
KRISTIN H. MAYFIELD AND PHILIP N. CHASE
JOURNAL OF APPLIED BEHAVIOR ANALYSIS
2002, 35, 105–123
NUMBER 2 (SUMMER 2002)

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.


Note: the effects of cumulative practice on problem solving.

Not "procedural fluency" or "automaticity" or "mastery" etc.

Problem solving.

The path to problem solving goes through a particular form of practice - cumulative practice - not through "do the problem 3 ways" (Trailblazers) or "explain how you got your answer."

Wednesday, January 3, 2007

learning math is hard

Update: For more one error detection and correction, take a look at this video (quicktime) starting at about 5:30. He's talks about error correction with reference to reading instruction. It continues on into this clip up until about 7:00 and math gets discussed for the last 3 minutes or so.

That's my current position based on teaching my six year old son math for the past year and a half.

Actually, that observation isn't based on my son having difficulty learning math. So far he hasn't. It's based on the the material we've skipped. It is that differential that separates the higher preforming math students from the lower performing math students. That differential represents an enormous amount of practice.

Unlike most parents who use Saxon to teach math, I'm using Connecting Math Concepts. Both programs are scripted, both use a mastery learning "basic skills" approach, and both have lots of practice built into the program. Both are complete programs which don't require parents to know how to teach math; knowing elementary math is sufficient. For most kids there is not much difference between the two. Contrast this with Singapore Math which does require some teaching skill to present and requires practice to be supplemented. That's not meant to be a knock against Singapore Math, each program has its strengths and weaknesses. I actually think that the ideal K-6 elementary math curriculum would be some combination of all three programs, capitalizing on the strengths of each.

For the purposes of this post, however, I want to focus on the practice aspect of learning math. To master elementary math a student needs to practice what's been learned until it is automatic. Unfortunately, most math programs do not provide sufficient practice to safeguard against the ravages of forgetfulness.

Most parents do not take control of the educational process until there the need to remediate becomes evident. At this point, there is a tension between the need to devote time for practice and the need to reteach the child to get him back on track as quickly as possible. Practice tends to get the short end of the stick at this point. It shouldn't.

One aspect I like about CMC is that it's been field tested so you can be certain that if the student has the math skills to enter a level of the program, the program will teach clearly enough and provide enough practice for the student to reliably master all the material presented in this level within one school year, about 120 lessons.

The most important aspect of CMC, however, is that error diagnosing and correcting are built right into the program, unlike almost every other math program. Let's face it, if students didn't make any errors while learning math, a trained monkey could teach math using almost any commercially available math program. It is in the diagnosing and correcting of student errors where most math programs fail. When students derail, many teachers are unable to get them back on the track. Math, being brutally cumulative is not forgiving at all when students derail.

This is CMC's greatest strength.

CMC is designed to minimize students errors in the first place by providing clear instruction in small instructional steps. Students are then tested frequently (workbooks are checked after every lesson and tests are given every two weeks) to check student errors. based on the ten unit tests, student errors are evaluated and a built-in remedy is provided to the student based on the errors the student made. The student is then retested to see if the remedy worked before the student is permitted to advance. If the student were permitted to advance without mastering the material, then the diagnosing and correction of errors would be become much more difficult come the next ten unit test because now the teacher doesn't know where the student went astray. Was it one of the new skills taught in the past ten lessons of was it one of the previously taught skills? Now extrapolate out 80 more lessons and try to figure out where the problem is for a newly taught skill that the student can't do. Forget about it.

Contrary to popular belief, the greatest shortcoming of the "constructivist" math programs is not the less than clear presentation of new skills, though this is certainly a problem; it is that error detection becomes virtually impossible. This is not so much a problem in a class full of higher performers, but it is deadly in a class where students make errors.

I see this post is getting a bit longish and I still haven't touched on the main point -- practice. So, I'm going to break it up into two posts since there's already much to chew on in this post. More to come.

Part two here
.