from the probably-where-I-went-wrong dept.
Educators, policymakers, and parents have begun to focus more on children's math learning in the earliest years. Yet parents and teachers still find it challenging to know which kinds of early math skills merit attention in the classroom. Determining how to help children achieve in math is important, particularly for children from low-income families who often enter school with weaker math knowledge than their peers. A new longitudinal study conducted in Tennessee has found that low-income children's math knowledge in preschool was related to their later achievement—but not all types of math knowledge were related equally. The findings suggest that educators and school administrators may want to consider carefully which areas of math study they shift attention to as they develop curricula for the early years.
Conducted by researchers at Vanderbilt University, the study appears in the journal Child Development.
The study followed 517 low-income children from ages 4 to 11; the children were primarily Black and all qualified for free or reduced-price lunch, a measure of poverty. When the children were in the last year of preschool and near the end of first grade, researchers tested general skills (including self-regulated behavior, work-related skills, and reading) and six math skills (patterning, counting objects, comparing quantities, understanding written numbers, calculating, and understanding shapes). When the children were at the end of fifth grade, researchers tested a range of math knowledge, including knowledge about numbers, algebra, and geometry. The aim of the study was to determine whether children's math skills at ages 4 and 5 predicted their math achievement at age 11.
Preschool math skills supported first-grade math skills, which in turn supported fifth-grade math knowledge, according to the study. In preschool, children's skills in patterning, comparing quantities, and counting objects were stronger predictors of their math achievement in fifth grade than other skills, the study found. By first grade, patterning remained important, and understanding written numbers and calculating emerged as important predictors of later achievement.
(Score: 2) by Runaway1956 on Wednesday December 07 2016, @04:17AM
How about plus and minus? It's just a wee bit early to start multiplication tables, or anything more advanced. If a preschooler can make change for a ten dollar bill (without the assistance of a computer), he is already ahead of most of today's high school grads.
(Score: 2) by maxwell demon on Wednesday December 07 2016, @08:21AM
By still insisting on the Fahrenheit scale, Americans deny their children early and natural access to negative numbers.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by Runaway1956 on Wednesday December 07 2016, @08:52AM
Huh? You seem to presume that all Americans grow up in the South. I had early access to negative numbers, in regard to the temperature. At 3 or 4 years old, I understood that -15 F was "colder than a witch's teat". Fortunately, or not, I never found the witch, so I never was able to see just how cold her teats were.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @12:11PM
All the ones that dont, do.
(Score: 2) by Kromagv0 on Wednesday December 07 2016, @01:17PM
Not in Minnesota.
T-Shirts and bumper stickers [zazzle.com] to offend someone
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @04:41AM
Just teach, measuring and testing has negative repercussions for the students themselves. We're too obsessed with providing ranking systems, each student is unique and we shouldn't still have such linear education models. Computer tech will free kids and teachers, kids can learn at their own pace and the teachers can focus on helping students learn and managing them more individually instead of focusing on repetitive demonstrations.
(Score: 2) by Runaway1956 on Wednesday December 07 2016, @05:24AM
Sounds like nonsense to me. How do you measure a child's progress, or determine what he needs to progress further, without testing? It's not just a "ranking system", after all. Teachers and parents need to know where the kid is at, to help him advance. Without tests and rankings, just HOW do you propose that teachers "focus on helping students learn"?
I don't care how "non-linear" your education system is, there will be tests, there will be grades and ranks. Unless you are planning for your education system to fail?
Besides - not everyone is a special snowflake. We don't all fall to pieces when we fail at something. A big fat F on a report card doesn't make anyone feel good, but it does help the more motivated students understand what they need to focus on.
(Score: 3, Insightful) by AthanasiusKircher on Wednesday December 07 2016, @08:06AM
Sounds like nonsense to me. How do you measure a child's progress, or determine what he needs to progress further, without testing?
You always need to have some form of assessment of skills, but that need not take the form of formal "testing."
It's not just a "ranking system", after all. Teachers and parents need to know where the kid is at, to help him advance. Without tests and rankings, just HOW do you propose that teachers "focus on helping students learn"?
Well, uh, you actually OBSERVE how the students do on their daily activities. When they succeed at them, you give them the next ones. It's really quite simple actually, and the way traditional "tutors" used to teach individual kids (and still do, I suppose, for some rich families). Formal testing is mostly adopted for two reasons, other than convenience of the teacher: (1) when class sizes are too large, it's difficult to give kids individual attention like that, and (2) with larger class sizes, the only way to make things workable is if kids are used to working independently. If you get preschool kids used to that system, they easily continue to do it throughout primary school. It's a lot harder to transition older kids if they are used to the "sit quietly in rows of desks and we'll all do the same stuff together" method of teaching.
I don't care how "non-linear" your education system is, there will be tests, there will be grades and ranks. Unless you are planning for your education system to fail?
My son went to a Montessori-style preschool with many of the free-form characteristics you claim can't work. Before he entered kindergarten, he was doing math and reading on basically an advanced 2nd-grade level.
I also lived in an area that had a public Montessori-style elementary school that you could be lotteried into. Kids there didn't receive "grades" -- they got written progress reports from teachers about the individual progress in various areas. They rarely had formal "tests," though they had sets of standards that they were expected to achieve each year... and teachers would steer individual students toward areas where they were lacking or needed extra attention to fulfill those basic standards. Students almost always went far beyond those basic standards each year, and they were basically allowed to explore as much as they wanted in whatever areas once they had achieved those standards. That meant that by the 5th and 6th grade, the school had to hire tutors from the honors calculus class from the local high school to come and tutor some of the middle-school kids in pre-calc and basic calculus, because those few students who chose to explore a lot more math had exhausted the algebra and geometry materials (as well as the teacher expertise) available.
The only time these students tended to all sit down and take a formal "test" together was when the state mandated testing came around each year or whatever. The school consistently scored in the top 10 primary schools in the state.
So, no, I don't necessarily think this is a recipe for "your education system to fail." It's just different from what most people are used to... and I don't think it can work everywhere. It needs special teachers who are trained in such methods and know how to organize a workable classroom environment. A lot of primary teachers could be trained to do stuff like this, but it gets progressively harder to implement in more advanced grades. (I taught for a year in a elite private high school -- one of those places that feeds a lot of students to the Ivy League -- and I had to adopt a more "free-form" and exploratory approach to my "conceptual" physics curriculum. It was tough at first, but ultimately a lot of fun. We did testing periodically, but a lot of other types of assessments too, mostly having to do with "lab" activities... which were themselves a lot more "free-form" than lab activities I had done in large public-school classes. But I could only do it because my class sizes were at most 9 to 12 students, and I had only four sections... well, three sections of conceptual physics, and one section of AP physics, where we did more traditional "testing" and such to prepare them for the AP. When I taught in public schools, I had about 5 sections of 25 students each... no way I could give that number of students individual attention like that.)
Besides - not everyone is a special snowflake. We don't all fall to pieces when we fail at something. A big fat F on a report card doesn't make anyone feel good, but it does help the more motivated students understand what they need to focus on.
The problem isn't the feedback itself. The problem is when all students are kept on the same track of the same activities, most of them are likely to be bored at some point. They're ahead in one thing, but behind in others. Neither in conducive to learning. If there's less stigma attached to the student who is "lagging" a bit in one area, and he can just keep practicing periodically until he gets it with individual activities, while ALSO doing more advanced stuff in something his GOOD at, overall it tends to work out.
I know this approach likely sounds foreign and even chaotic to people who aren't used to it. Indeed, when I visited my son's preschool, it seemed like chaos at first glance -- until you realized you had a bunch of 3-year-olds and 4-year-olds and 5-year-olds each going around, picking up materials for activities they liked, placing them down on their own mats (which everyone was taught to respect in the first couple weeks -- it was critical for all of them to respect each other's workspaces... I still don't know how the teachers managed to get that all working), and then working on independent activities with the teacher and a teaching assistant wandering around and giving encouragement, showing new things, pointing out errors, etc... it was astonishing. But it seemed to work. A lot of it in that case also has to do with the way the Montessori activities are designed to allow that sort of engagement for individual kids.
If I hadn't seen it with my own eyes, I'd have thought it was a magical fairytale too.
(Score: 2) by AthanasiusKircher on Wednesday December 07 2016, @08:22AM
Oh, I realized I should note that my son was a bit of an outlier at his Montessori preschool, BUT it did seem like many of his classmates were already working on stuff that was closer to advanced kindergarten or even 1st-grade materials before they finished the preschool curriculum. And actually the school also had an intermixed preschool and kindergarten classroom (3-6 year olds), so the kids that were more advanced just learned activities with the "kindergarten" students. It wasn't ALL completely individual: the teachers would commonly pair students up in groups of 2-4 who were near the same level in a particular skill to work on a new activity together. (That's the only way I can imagine that could manage teaching so many students at different levels at once.)
(Score: 3, Informative) by VLM on Wednesday December 07 2016, @02:05PM
and the way traditional "tutors" used to teach individual kids (and still do, I suppose, for some rich families)
The traditional name for that was "parents" not tutor. Even as recently as a decade or so ago I sometimes feel I taught my kids math, not the schools. They tried, but there's a production difference between 1-to-15 in the classroom (OK, rich district, whatever) vs 1-to-1 doing homework with Dad.
And the plural "parents" matters because centuries/millennia of kids were raised in families that had an absolute minimum of two adults, and now one is pretty common almost majority and is majority in poor areas, and aside from all the touchy feely BS, some of which might be correct anyway, it is self evident that kids with two parents obviously have twice the odds vs single parent that someone in the house can teach them any individual subject.
(Score: 2) by VLM on Wednesday December 07 2016, @02:25PM
public Montessori-style elementary school that you could be lotteried into. Kids there didn't receive "grades" -- they got written progress reports from teachers about the individual progress in various areas.
My kids were at the leading edge of attending a public "STEM Academy" back when that was new and cool and people seem to be doing exactly the same thing but calling it "STEM" instead of "Montessori". I sometimes wonder what the non-STEM special teachers thought about "STEM" report cards when filling out their section for elementary gym, music, art in the "STEM" style but not themselves being science or math teachers...
I believe there is also a parallel between report cards and corporate groupthink WRT annual evaluations, where decades ago it was like one piece of paper (if that) and there's a trend now to have corporate evals be like 15 pages of values and skills BS.
From memory the last report card my daughter got from that elementary school was like an 8 page pdf file online. The detail level was crazy like is she progressing or proficient or advanced at adding two digit negative numbers to three digit positive numbers without carries or whatever. Gym section was similar, she was progressing at shooting baskets but advanced at dribbling the ball, developing at the long jump, proficient at the 50m run, etc. The kids didn't seem to have any problem transitioning to "real grading" when they got older, at least not that I observed or heard from the other parents.
I'm old enough to remember report cards being computer dot matrix printed postcards sent in the mail, at least by high school. If I recall the teachers had a 30 or so character comment field, for those who think tweets are too verbose and wordy.
Pessimistically I could predict that some of the wordiness of new style report cards is its harder to think teachers do nothing if whats produced to the parents is a short term paper rather than a letter and a nano-tweet like I got as a kid. "Look how great our schools are we sent home over 20K pages of paper in the form of report cards per year". Length of report card likely correlates positively with taxpayer impression of how well the schools are doing, even if nothing changes from the kids perspective or experience.
(Score: 2) by AthanasiusKircher on Wednesday December 07 2016, @08:21PM
My kids were at the leading edge of attending a public "STEM Academy" back when that was new and cool and people seem to be doing exactly the same thing but calling it "STEM" instead of "Montessori".
Just to be clear -- I don't know precisely what was involved in your "STEM academy," but Montessori is a very specific teaching method that involves a bunch of very specific materials (lots of physical activities with "manipulatives," etc.). They're often private and more expensive due to the cost in acquiring all these specialized materials. Ironically, when the founder of Montessori originally came up with this stuff, she made simple things out of stuff like wood, which was intended to be CHEAP back then. There's also a lot of very specific Montessori dogma regarding exactly how you introduce activities and concepts, how you lead children from one thing to another, the "proper" way to do every activity, etc.
I personally don't buy into the dogma that much, and while I think a lot of the physical materials for the activities have a sound pedagogical basis, I think a lot of schools and teachers who do this go overboard in fetishizing these teaching materials and methods as if they were the only way that works.
Nevertheless, if you're looking for a more individualized approach to primary pedagogy, the local Montessori school may be the only one available for a lot of people. If your kids had an opportunity to do similar things without all the Montessori dogma (whether at a "STEM academy" or just at a better public school), that's really cool. My son also ended up attending a public kindergarten which was NOT Montessori, but it was also a lot more individualized than my kindergarten experience, with various "learning stations" and activities that kids were given more freedom to explore.
Pessimistically I could predict that some of the wordiness of new style report cards is its harder to think teachers do nothing if whats produced to the parents is a short term paper rather than a letter and a nano-tweet like I got as a kid.
As someone who actually had to write those "progress reports" at the private high school I mention, I have to agree a bit. I ended up "padding" them a lot, frankly, just because it seemed to be expected. (And in this case, the parents were also paying a rather huge tuition too.) In most cases, a short paragraph would have been plenty to say how the student was doing in my class for that quarter, but it seemed like a more lengthy "letter" was the expectation.
(Score: 2) by VLM on Wednesday December 07 2016, @09:14PM
but Montessori is a very specific teaching method
Oh right on right on, I agree with you in that area, I meant specifically WRT the style of the progress reports. Not necessarily the rest of the secret sauce. Although watching my kids and trying to remember back when I was a kid specifically WRT manipulatives they seem to be more "into that" in the 00s/early 10s than they were in the 70s. Its not like the world suffered a lack of poker chips or legos in the 70s but I don't remember using them as much as I saw my kids use them.
Possibly some kind of convergent evolution thing going on with report card format, given similar outlooks or training the format of report cards tends to converge no matter if "public STEM academy" or private Montessori.
Speaking of convergent evolution Kumon originally evolved to use cheap worksheets but the monthly rate for Kumon isn't that cheap. Perhaps the (tm) (c) (r) worksheets the franchises buy are not cheap.
You have a lot of interesting inside education information which is cool. My SiL and a cousin both work as school teachers but they never talk anything of substance just complain mostly, in fact they complain a lot, unfortunately.
(Score: 1) by kurenai.tsubasa on Wednesday December 07 2016, @02:38PM
You proposed a good pass/fail test above. See if they can make change for a $10 bill. Then throw a total of $7.85 at them where the customer pays with a $10 and a dime, etc.
I think one problem is we have these big nebulous categories like “reading” or “maths.” So then we get nebulous advice such as students need to spend more time learning reading! Students need to be better at maths! Which math?! Reading what?! So I'd propose instead of humongous standardized tests—I wonder if test week is still the week you get OJ at your desk because research shows that OJ gives a +2 to int and you also get to listen to classical music since that gives another +2 to int— why not smaller pass/fail tests to establish overall progress like making change?
As far as letter grade, I'm of a divided mind about that. Maybe if we go with, at the elementary level, a progression of those small tests. Get rid of the OMG it's test week! Then create some criteria such as an A student can make change in all situations within say 30 seconds, can summarize a story in their own words, and can name the capital of any given state. Degrade from there until we get to F which would represent current high school graduate ability lol.
(Score: 2) by Runaway1956 on Wednesday December 07 2016, @03:27PM
You remind me of a once common occurrence. My bill comes to $7.25, so I offer a ten dollar bill, and a quarter, expecting three dollar bills in return. At some point in time, the understanding that I would prefer to get a quarter OUT OF my pocket, instead of putting three additional quarters INTO my pocket was lost. Nowadays, the kid at the register just looks at you crosseyed, like he thinks you're retarded. He will make change for that ten dollar bill, then push the quarter back across the counter at you. I guess he doesn't know how to punch 10.25 into his computerized cash register.
And, that kind of stupidity has influenced the size of the tip I may have left. Good grief, why reward stupidity?
(Score: 0) by Anonymous Coward on Thursday December 08 2016, @03:30AM
Gee, that doesn't happen to me -- Western NY State. Move to a smarter part of the country. Maybe that's what it will take to improve your attitude(grin>).
I'm always handing the "cents" part to cashiers (kids, adults, whoever) and they always get it right.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @06:06AM
Computer tech will enslave and abuse kids and teachers, unless schools stop using non-free proprietary user-subjugating software. Want to view the source code to see how the software works? You can't because it's proprietary. Want to make a change to the software? It's proprietary, so you can't. Want to hire independent developers to make changes to the software so that it can better serve the school? Not happening: It's proprietary. Now that's how you encourage education, freedom, and critical thinking!
If that's how it's going to be--and that looks to be the case--let's just stick with paper and pencil.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @06:10AM
Oh, and let's not forget the way many schools are forcing their students to give their names to companies like Google, who then collect data about them. Supposedly the companies won't abuse the data, but even in the unlikely case that that's true, the data collection is already intolerable. It should be outright illegal for schools to violate kids' privacy like that; either they develop their own systems or they simply don't use one. It's not just a matter of free vs proprietary software.
You talk about computer tech without considering the implications.
(Score: 1) by anubi on Wednesday December 07 2016, @07:51AM
I think that companies, like religions, are trying their damndest to get it into the kid's mind of how they want the kid to grow up thinking... that is they want business-friendly paradigms in place to work for peanuts, do as they are told, surrender their rights and privacy, but respect the rights and privacy of others.
Because they say so.
You know, the cognitive dissonance thingie that you want your engrams in their mind first so later stuff has the hurdle to overcome to displace.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 1) by anubi on Wednesday December 07 2016, @07:42AM
That is exactly why I was trying to teach the neighbor's kid algebra using GWBasic.
He already knew arithmetic, but the tedium of all that arithmetic crank turning was terribly distracting while trying to demonstrate the abstract concept of letting a variable name represent a number. GWBasic was just the tool I needed to illustrate the concept of letting some name be a number, and solve for it.
And, at the same time, illustrate how to present a math problem to a computer so it can help him.
We found an old laptop, I loaded it up with DOS, GWBasic, MathCad, Borland Eureka, VisiCalc, and a few other old-school proggies so he could use it do arithmetic - freeing him to explore what he was doing without having the tedium of actually doing it. I do not feel its necessary to learn carpentry using a brace and bit. Use the electric drill. Nothing much of value was learned spending ten minutes to get a hole made in a piece of wood anyway. The real skill was in knowing where to put the hole.
I sure would have liked to have had GWBasic available to me when I first was learning algebra, calculus, circuit analysis, and thermodynamics, just to relieve myself of the tedium of all that arithmetic. I hated thermodynamics when I first messed with it because of my intense dislike for interpolating steam and logarithm tables - now I love to work with thermodynamics, cause now I get to explore concepts and let the computer do all the messy arithmetic.
Yeh, I know its ancient technology, but I predate even that. At one time in my life, that stuff was new. And it was new after I had my degree in hand. This is an old dinosaur that lived in the day of the vacuum tube, morse code, and winding your own coils. I mean really old-school. In a way, its amazing I am still running.
"Prove all things; hold fast that which is good." [KJV: I Thessalonians 5:21]
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @03:27PM
You know that GWBasic and DOS are also non-free software? Sure, you're not likely to be sued today for making copies, but that doesn't make it any less proprietary.
Besides, Python isn't harder than GWBasic when only using the basic features (no pun intended).
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @05:06AM
This is nonsense. There are many biases, most notably the parents - parents who hassle their toddlers into learning how to count will hassle their teenagers into learning how to do calculus.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @06:02AM
There should really be a 'social science' warning on articles like this.
(Score: 2) by tfried on Wednesday December 07 2016, @07:14AM
True, the study does nothing to establish causality. A "real" test would be to research the effect of (randomly assigned) programs. But that is simply a heck of a lot more difficult to accomplish. My personal guess on this is that they may be on to something about the importance of "comparing quantities" and "counting". Lack of a basic understanding of quantities may well be at the heart of Dyscalculia [wikipedia.org] for instance. Children lacking in that area will understandably have difficulty keeping up (while - notably - Dyscalculia does not necessarily imply that students will have difficulty with the "memorizable" parts of maths, including basic calculations). I don't see any particular reason to assume that this ability should not be accessible to early training.
On the other hand, "patterning" looks quite a bit like your regular (maths / logic) intelligence test to me. Quite obvious that this should affect maths achievement even years later. Quite dubious that training can achieve much beyond an initial "so that is how to approach these exercises"-effect.
Perhaps, what is a more important insight from the study, however, is what they did not find to be related to later achievement: understanding shapes. From my personal - hazy - recollection, that made up quite a big share of preschool "maths", and here's indication that this time might better be devoted to something else...
(Score: 2) by maxwell demon on Wednesday December 07 2016, @08:35AM
I think it depends a lot on how many patterns you already know and therefore can recognise immediately. A larger "library" of patterns also means you've got more material to recognise "meta-patterns" (those need not be at a level that you could explicitly tell them, it just matters that they are available to your "pattern matching engine") that help you recognise new pattern.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @12:30PM
> True, the study does nothing to establish causality.
But TFA heavily implies causality. Junk reporting (I didnt read the paper, I assume the authors did not imply causality but social scientists meh).
> A "real" test would be to research the effect of (randomly assigned) programs
I understand meta-studies have shown that no matter what program you put students into, it demonstrates achievement while the paper is being written. When those programs are rolled out, the improvement is much more muted. The interpretation is that just putting researchers into the school causes improvement irrespective of what the researchers are doing.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @03:43PM
The same is true of classroom discipline studies. It doesn't matter what system you use to run the classroom, but you will see improvement over the control group, apparently because the research is being conducted.
When I was in ed school (thank God I got out of that shithole of insanity), I looked into one such study and found that the author of the study had dropped about half his initial data because it did not confirm that the system he was testing actually improved classroom discipline. It probably didn't help that the researcher was also selling the system as a set of books and seminars. Demonstrating that his system worked meant money in his pocket, so dropping data that showed no improvement over the control group meant bolstering the case for schools to hand him more money. I have no doubt that such methodology is at play in many education studies. There are more "methods" and seminars being sold in education than in used car sales, and they're of about the same quality. Education research will continue to suck as long as the researchers are seedy salesmen pushing their products rather than dispassionately measuring results.
(Score: 2) by tfried on Wednesday December 07 2016, @08:02PM
The interpretation is that just putting researchers into the school causes improvement irrespective of what the researchers are doing.
Well, yes and no. The takeaway is to never compare an intervention (program) to no intervention, but at least a credible dummy. Not entirely unlike giving a placebo to control subject in a medical study, instead of just nothing. Of course in order to be a credible comparison, you'll need to put in roughly the same amount of professional involvement, which means you've just doubled an already high cost.
That's not really an excuse for cutting the corners, but sometimes an unavoidable reason for doing it despite knowing better...
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @01:26PM
Yeah. Math is for pussies.
(Score: 0) by Anonymous Coward on Wednesday December 07 2016, @03:24PM
Only 4 to 11? Most studies about these kind of early-education topics show gains in grade school, little gains in junior high, and any gains are gone by the time they hit high school. If there's not a followup study in a few years that covers the rest of their primary education, this study was done for ideological rather than scientific reasons.