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07 Mar 2006 - 18:12
I think Ken left a link to this study awhile back, but I have no idea where it is, and I don't think I wrote it down anywhere, so I'lll start with this:
Reports on college literacy levels sobering
'Study: Most students unable to handle complex but common reading tasks'
More than 50 percent of students at four-year schools and more than 75 percent at two-year colleges lacked the skills to perform complex literacy tasks. That means they could not interpret a table about exercise and blood pressure, understand the arguments of newspaper editorials, compare credit card offers with different interest rates and annual fees, or summarize results of a survey about parental involvement in school.
3 forms of literacy
worst area is math
The survey examined college and university students nearing the end of their degree programs. The students did the worst on matters involving math... Almost 20 percent of students pursuing four-year degrees had only basic quantitative skills. For example, the students could not estimate if their car had enough gas to get to the service station. About 30 percent of two-year students had only basic math skills.
what they could do from the CBS News account:
Most students at community colleges and four-year schools showed intermediate skills, meaning they could perform moderately challenging tasks. Examples include identifying a location on a map, calculating the cost of ordering office supplies or consulting a reference guide to figure out which foods contain a particular vitamin.
in a nutshell
college accountability? There's been talk lately of holding colleges accountable. I haven't followed it, but it's out there. The AIR study of college student literacy reminds me of an obit I read when Peter Drucker died. The writer said that Drucker had made many correct predictions in his lifetime, and that his main prediction lately had been that colleges as we know them would cease to exist. Unfortunately, I don't seem to have saved the article, but a new article by Walter Russell Mead is about the same issues:
Paying for college education is one of the biggest financial worries facing middle class and working families.... ...perhaps [government] could offer an alternative: a federally recognized national baccalaureate (or 'national bac') degree that students could earn by demonstrating competence and knowledge. With input from employers, the Department of Education could develop standards in fields like English, the sciences, information technology, mathematics, and so on. Students would get certificates when they passed an exam in a given subject. These certificates could be used, like the Advanced Placement tests of the College Board, to reduce the number of courses students would need to graduate from a traditional college. And colleges that accepted federal funds could be required to award credits for them. But the certificates would be good for something else as well. With enough certificates in the right subjects, students could get a national bac without going to college. Government agencies would accept the bac as the equivalent of a conventional bachelor's degree; graduate schools and any organization receiving federal funds would also be required to accept it. Subject exams calibrated to a national standard would give employers something they do not now have: assurance that a student has achieved a certain level of knowledge and skill.
This is a long excerpt, so I'll put the rest of it here.
Without having thought about it, I'm in favor of anything that increases the public's knowledge of what students are actually learning in school.
National Assessment of Adult Literacy
"A nationally representative and continuing assessment of English language literacy skills of American Adults"
key findings of NAAL
AIR press release
complete AIR study here
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If more than 60 percent of 4-year students, 75 percent of 2-year students, and 85 percent of the adult population in general cannot:
Almost 20 percent of students pursuing four-year degrees had only basic quantitative skills. For example, the students could not estimate if their car had enough gas to get to the service station. About 30 percent of two-year students had only basic math skills. This may depend on the form of the test. My mental arithmetic was stuffed by the end of engineering school - all the maths I had done for the last three years was either algebraic (I had pages and pages of notes where the most complicated actual number was a 2), or complex enough and/or involving enough sin and other calculations that I just did it by calculator. When I went job-hunting I had to retrain myself on basic mental arithmetic. I knew how to do it in my bones, but I was very slow. -- TracyW - 07 Mar 2006
"Students would get certificates when they passed an exam in a given subject." ...which used to be called a High School Diploma. -- OldGrouch - 08 Mar 2006
I heard somewhere that those uni courses where a professional body was involved in judging a degree have retained their rigor, while the degrees that don't have that external quality control have gotten easier as more and more people have gone to uni. For example, a sign of being a professional engineer is being a member of the IEE or IEEE, and being a full member of one of those two groups is dependent on having a degree in engineering from a university approved by them, so engineering schools have an incentive to maintain a tough degree to meet IEE and IEEE's requirements (and IEE and IEEE maintain tough requirements becuase they want to keep the suplly of new members relatively low to maintain the prestige of membership for their existing members.) -- TracyW - 08 Mar 2006
I heard somewhere that those uni courses where a professional body was involved in judging a degree have retained their rigor That's interesting. This is a Big Question for me - how does one maintain standards over time.....? One of the concepts behind NCLB is that 'sunshine' & transparency help a great deal, which is why I'd like to know, EXACTLY, what Christopher is supposed to be learning at school. If concise & easily understandable information were INSTANTLY available and accessible to everyone about what the standards actually are, I think that would have an effect.... -- CatherineJohnson - 08 Mar 2006
I'll find that Brookings paper at some point & post the relevant passages.... -- CatherineJohnson - 08 Mar 2006
I was tutoring a student in the Basic Math class today. This is the class that goes over basic math from 4th grade stuff (division and fractions) to pre algebra. It is the only class in the college that does not allow a calculator. She was learning about percentage. The word problem was this: A company has 280 executives. 11% have cell phones. How many executives have cell phones. She didn't know how to do this and didn't understand my explanation. So I said, "If you and your friends went out to dinner and spend $30 and wanted to leave a 10% tip (small, I know but I wanted to use easy numbers), how much would you have to leave?" I figured I could equate the 10% times 30 to the 11% times 280. She just looked at me very puzzled. "Are you asking a real question?" "Yes,", I said, "how do you know how much to leave for tip?" She said, "One of my friends always tells me what to leave." That is the state of math litercy. -- AnneDwyer - 08 Mar 2006
whoa you know, I'm not surprised. I was wondering just yesterday how many people can compute tips these days. -- CatherineJohnson - 08 Mar 2006
Anne try the Saxon method with your students (AND BAR MODELS - Saxon often uses bar models to teach percent) I had Christopher doing practice percent problems last night ('what number is 25% of 40? etc.) & he WHIPPED through them using the Saxon set-up. The worksheet was terrific, because they had all 3 variants on the same sheet:
Saxon method for setting up percent equations I just found something incredibly cool. On February 19 Christopher couldn't begin to do this problem. Christopher is studying algebra in the 6th grade, but he can't do percents. I pulled the Sample Test, which turned out to be the test Christopher's class took this week, and asked him about problem number 26:
On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot. Part A What percent of the total number of cars were in the parking lot on Friday? Show your work. Part B What percent of the total number of cars were in the parking lot on Saturday? Show your work.
Last night he WHIZZED through those percent probems - and he did a couple of word problems with some ease as well. I'll give him this one again tonight, and see how he does. I bet he can do it. I haven't used bar models for percents in the past two weeks. I've used the Saxon-Dolciani-Brown ratio-proportion charts & the Saxon WN equations.
-- CatherineJohnson - 08 Mar 2006
I was teaching Christopher Lesson 77 in Saxon 8/7 today: "Percent of a Number, Part 2." Saxon does something incredibly cool. He gets kids started on writing equations to solve very simple fraction & percent problems by using WP, WN, WD, and WF to mean "What percent?" "What number?" "What decimal?" and "What fraction?" Take the question:
What percent of 40 is 25?
The 'of' translates easily & directly to x; the 'is' translates easily and directly to =; the 'what number' translates to WN: WP x 40 = 25
What number is twenty-five percent of 80?
This system allows Saxon to teach percent, decimal, and fraction problems close together, without students getting lost mid-stream. (At least, I assume this system works....it worked with Christopher today, so he's my 'n of 1.')
-- CatherineJohnson - 08 Mar 2006
-- CatherineJohnson - 08 Mar 2006
Last night Christopher was bypassing the charts and going directly to the proportion - and he did it right. Plus he set up one problem in a way I thought was wrong, but turned out to be correct. I bumped into another 'hyperspecific' knowledge-fragment..... -- CatherineJohnson - 08 Mar 2006
The Saxon lessons in 8/7 are great for the strugglers. I think it's also in 7/6. It really takes you by the hand and goes slow, starting with easy, obvious ones until the procedures become more automatic, and then moves to more complicated ones. Edhelper.com has a lot of worksheets on converting back and forth between decimals, percentages and fractions, from easy to hard. They also have the hundred square boxes to show the visual of something like 21/100 or .21, which are good for early introductions to the idea. It re-inforces how they relate, but isn't too difficult (no division at that point, necessarily) Also, the foundation of using the exact same number line for fractions for several chapters and then later for decimals is just another good visual to support the idea that these things are the same things, written in different form. I think that the way these concepts (fractions, percentages, and decimals) are being glossed over more and more is possibly contributing to the idea that they're all separate and different concepts entirely. Also, place value is re-inforced before relating decimals to percentages, and I think this made a huge difference with my LD son. -- SusanS - 08 Mar 2006
They also have the hundred square boxes to show the visual of something like 21/100 or .21, which are good for early introductions to the idea. Thanks for the tip. Are these in middle school math or elementary math? -- CatherineJohnson - 08 Mar 2006
Also, the foundation of using the exact same number line for fractions for several chapters and then later for decimals is just another good visual to support the idea that these things are the same things, written in different form. I think that the way these concepts (fractions, percentages, and decimals) are being glossed over more and more is possibly contributing to the idea that they're all separate and different concepts entirely. Absolutely. The Saxon books are so careful and respectful. -- CatherineJohnson - 08 Mar 2006
'Respect' is the main feeling I get from Saxon. The student as always being addressed as a serious person, whose learning matters to the author. -- CatherineJohnson - 08 Mar 2006
There are no admonitions, scoldings, or pep talks — just the wonderful formal 'exhortation' at the beginning of each book! I'm going to get that typed up and posted one of these days. -- CatherineJohnson - 08 Mar 2006
When I started re-learning math I realized that I really didn't understand place value. I kind of saw it as semi-arbitrary: ones, hundreds, thousands.... -- CatherineJohnson - 08 Mar 2006
I have teeny print, Catherine. Is yours teeny? When I started re-learning math I realized that I really didn't understand place value. Me neither. I thought I did, but I didn't. It sure makes a difference when teaching new concepts, though. The hundred boxes are probably in 4th/5th grade math. If you can't find them, let me know and I'll dig them up. I have some sheets upstairs so I can always just find the address. If you go to 4th or 5th grade math and go passed the mixed worksheet stuff onto the skills (that you can just click on), then find decimals. I think it should say something like "tenths" or "hundredths" and then "with graphic." They also have sheets where they use numbers and words and then have you write the correct decimal. The one my son did last night had around 40 quick problems. Several ones were things like "forty-six hundredths" or "three hundredths." Others were in fraction form either over 10 or 100 and then they have to just write the decimal. My son just needs that extra practice over and over to solidify the relationship. -- SusanS - 08 Mar 2006
uh-oh let me look you mean up front? -- CatherineJohnson - 08 Mar 2006
I thought I did, but I didn't Me, too! I'm pretty sure I found some nice hundreds charts online, too... -- CatherineJohnson - 08 Mar 2006
hmm maybe not I made my own for Andrew (wonder if it's too big to load?) -- CatherineJohnson - 08 Mar 2006
Teeny font starts right at the comments. Your name is tiny right after the ratio boxes. Or maybe it's just me. -- SusanS - 08 Mar 2006
weird I better check this on another browser it's fine on Safari -- CatherineJohnson - 09 Mar 2006
I just added a font size command. Does that make it any different? -- CatherineJohnson - 09 Mar 2006
Two things: 1) I think that spending a little time with number bases other than ten (e.g. base 8) helps highlight place value. It also ties in positive and negative exponents as you label the place value columns as powers of the base. 2) I think it was an old Prentice-Hall math book that had a good way to set up percent problems. You use a box divided into four quadrants. The upper left quad is labeled "part;" the lower left is labeled "whole;" the upper right is "%;" and the lower right is the number 100. As you read the percent word problem, you fill in the box, placing an x in the space for the desired unknown. For example, 18 out of 30 students in a class are girls. What percentage of the students are girls? You identify 18 as the part; 30 is the whole; and x goes in the % box. Then you have your ratio set up as the left half of the box equal to the right half of the box: 18/30 = x/100 Then, solve for x. x = 18 * 100 / 30. I think you get it from there, but I'll do another example: Of 240 people surveyed, 24% said that red was their favorite color. How many people chose red as their favorite color? 240 is the whole; 24 goes in the % box; and x goes in the part box. This leads to the equation x/240 = 24/100. x = 240 * 24 / 100. -- DanK - 09 Mar 2006
Oops! Bad example. Let's make that 30% of 240 people like red. I hate ending up with fractional people. -- DanK - 09 Mar 2006
1) I think that spending a little time with number bases other than ten (e.g. base 8) helps highlight place value. It also ties in positive and negative exponents as you label the place value columns as powers of the base. I agree! Saxon 6/5 teaches Base 5, as I recall. I found it very helpful, though I needed more time and practice with it. In fact....now that you mention it, I would make this a principle. The way to go, I think, is to use Base 5, because you can use pennies, nickels, and quarters - there's already some familiarity. (Parker & Baldridge have a number of Base 5 exercises in their book for elementary teachers using Singapore Math.) -- CatherineJohnson - 09 Mar 2006
Dan I love that Prentice Hall example - perfect. I'm going to teach that to Christopher. It does a much better job of getting the meaning of percent problems across than the Saxon WP equations. The equations are fantastic, and they do a great job teaching the translation of simple questions into equations. They also are a fabulous Working Memory aid. At the end of a problem the child can see that his answer is supposed to be a percent, or a fraction, or a number. (Very, very often, by the time they've gotten to the end of the calculation, kids have no idea what they were looking for.) But the Prentice-Hall set up teaches the concept, too. -- CatherineJohnson - 09 Mar 2006
It's still tiny. I can read it fine, though. Am I the only one? I have Yahoo. -- SusanS - 09 Mar 2006
A sub tag wasn't closed. -- RudbeckiaHirta - 09 Mar 2006
Tag closed. -- DougSundseth - 09 Mar 2006
Shameless self-promotion. I have a page on my site that has an introduction to place value in trying to show how braille cells can be thought of as binary numbers. http://www.dotlessbraille.org/numbersystems.htm -- SusanJ - 09 Mar 2006