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math struggle pic

To recap Part I and Part II, we learned that reading scores on the NAEP tests have not improved significantly in 40 years and that any gains have been mainly due to raising the scores of the lowest percentile groups and minority subgroups.  We learned that 17-year-olds made no statistical gains whatsoever.  We learned that Whites have not seen a significant rise in scores and that Catholic school students outperform even the White subgroup of public schools.  We learned that poverty rates do not and cannot explain the lack of proficiency in the United States in math and reading; not entirely and not primarily.

Next, I am going to present the Long Term NAEP results for math in the same format as I did in Part II for reading.

Math Results

overall math trend 2012

Reminder:  Clicking on the charts and graph will bring up a window where these items can be viewed in more detail.

These are similar trends as observed in the reading scores except that the scores in math started out higher and finished higher. Notably, the higher scores at the 9- and 13-year-old level do not carry over into the scores of 17-year-olds, just as they did not in reading.

scoregains 17 math

As with reading, by the time 17-year-olds take the math test, only the lowest percentiles experience significant gains, and this is what the study chooses to highlight.  However, the 9 and 13-year-olds realized higher gains in math at all percentiles than observed for reading.  That is good but only speaking in relative terms.

black white math gap 9

black white math gap 13

black white math gap 17

As with the reading scores, the Hispanic score gap, though not shown, mirrors the trends observed in the Black gap trend.  And, as with the reading scores, any math gains realized at the 17-year-old level were negligible in Whites and only 18 points in Blacks.  Most of the gains across all age groups were made by Blacks and Hispanics. The one positive difference was that 9 and 13-year-old Whites improved their scores more in math than they did in reading.

catholic public gap 9 math

catholic public gap 13 math

catholic public gap 17 math

When looking at the same data for reading, I compared the public vs. Catholic school scores to those delineated for each age group based on what grade the students were at in school.  This data was not put into table format in the NCES report, but a search of the online database indicates the following:

math grade level

Whereas the upper grade scores were lower than the Catholic school scores in the reading analysis, the upper grade math scores of all students (which includes Catholic students) is roughly equivalent to the Catholic school scores for 9- and 13-year-olds.  The lower grade scores for math, like in the reading analysis, are roughly the same as what the Black subgroup scored in the 9 and 17-year-old studies, though Blacks still scored 10 points below the lower grade (7th grade) 13-year-olds.

These differences suggest to me that even relatively well-to-do white people cannot overcome Whole Language deficits, but being white greatly improves your chance of performing well (relative to other groups) in math at the younger ages.  But as with the reading scores, being white will not help much to improve the math scores of 17-year-olds.  Yet those Catholic school students, who also tend to be educated in more traditional ways, outscore public school students at 17 years old by 20 points and White students by 13 points.  I suggest that any perceived “successes” in math at the lower grades has evolved because parents at the lower grades are putting in much more physical time working with their children to overcome the deficits in instruction and mastery at these age groups.  Even so, this extra parent involvement does not mitigate the long term damage as demonstrated by lackluster 17-year-old scores.

This can’t just be poverty.  It has to be instruction, curriculum, or some other outside influence or a combination of these factors.  Catholic schools prepare students to achieve higher scores on these tests even while spending 32% less than public schools per student.

The following table is four years out-of-date, but still shows the relative cost of public school compared to Catholic and other private schools.

cost per pupil comparison

The most recent cost data for Catholic schools is below.

per pupil cost catholic

After considering the total number of students enrolled in elementary and secondary Catholic schools, the average cost per pupil in 2012 is $7,263 compared to $10,652 in public schools.

The following shows how well religious and independent school students perform on another test, the SAT, compared to their public school counterparts.

sat results 2011

Religious-schooled students perform 82 points higher in critical reading, 27 points higher in math, and 45 points higher in writing than public-schooled students while spending less money. Those students in expensive independent schools score even higher, but their 70% higher costs only translate into 15% – 20% higher scores while religious schools score between 5% -18% higher.  As you will recall, Catholic schools spend 30% less than public schools. The stripped down take-away is that however Catholic schools are teaching, both public schools and the expensive private schools should take a look at their education model.    I also think that it becomes clear where money helps most above and beyond what is potentially curriculum – Math.  The independent schools have a 45 point advantage over even the religious schools.  This is likely due to expensive private tutoring on top of expensive instruction, because the critical reading and writing scores were not raised as significantly in the independently-schooled students.  Obviously money matters in education.  Bottom line, though, is that public schools will never have the resources of independent schools, so why not teach like Catholic schools while making the most of the 30% more funding public schools enjoy.

Now back to the NAEP data.  I must admit the math results for public schools are somewhat confusing.  There were a lot of gains in scores of the poorer minority groups since the 70s just as there were in the White subgroup at the 9 and 13-year-old levels even if the gains did not move the majority towards proficiency in either math or reading.  It has been my belief that the progressive education system works best for those in higher socio-economic classes, so why the gains in what is presumably the lower socio-economic groups?  It is possible that the progressive math curriculum has worked to move minorities over a crucial threshold, but then stalls, moving fewer students of all subgroups towards proficiency.

Whatever the reasons behind the incongruity between what is observed at the lower grades versus what is observed at the upper grades and even in college, it is obvious that we need to take a serious look at our math and reading curriculum (and probably science as well).  I can say with a high degree of confidence that if the progressive curriculum is designed to make children think more critically, to the extent that it is being used in schools, it is not working very well meeting that objective.

Take the following questions released from the NAEP math test given to 17-year-olds in 2012:

simple algebra 2

Only one-third of 17-year-olds answered this question correctly.  Let that sink in.  Now consider that over half of the students chose the wrong answer “C”.  Given the convoluted second suggested solution, I guess I can understand why students taught this way might make this mistake.  Why not just teach kids how to solve for A?  The correct answer MUST satisfy this truth:  some number “A” divided by 40 equals 120, and that same number “A” divided by 80 must equal the number the student chooses as the answer; which on this test, the majority of students incorrectly chose as 240.   There is no good way to check the reasonableness of the answer unless you know how to solve for A, and clearly the ½ trick backfired.  Heck, whoever is preparing these kids to take a standardized test is not even doing a good job teaching to the test.

Here is another example of poor analytical skills.

rectange angles question

Side note:  Let me assure the reader that I DID NOT choose answer D as this screen capture suggests.  I chose the correct answer E, but for whatever reason, the NCES site will not recognize the correct answer E no matter how many times it is chosen.  Try it.

This is another one of those questions that should not be missed if students are checking their work.  I understand why almost 20% chose answer “C” because they were thinking triangles (that was even my very first thought), but I was also taught to look at all the answers even if I think I know the correct one right away.   And in doing so, I realized my hasty mental conclusion was not for a rectangle which has  four 90 degree angles; four times 90 is 360 NOT 180.  Granted, more of the students answered this one correctly than the previous question, but still, it is really easy and takes more common sense than it does math ability.

This next question blows my mind.

percentage question

The progressive math curriculums I’ve seen all stress rounding to determine reasonableness. While I think the curriculum teaches rounding in a dangerous way, this particular problem practically screams for rounding to be employed.  56% is about 50% which is the same as one-half (that is some of the most basic math taught in 4th grade).  So, half of 20 is close to 56% of 20.  Half of 20 is 10 (at least 2nd grade math).  Therefore, the ONLY answer that can satisfy this criteria is A.  The other answers are not even tricky, they are just outrageously wrong.  Only about ¾ of the students got it right and almost 20% said that 56% of 20 is GREATER than 20.  OMG!!!  Shouldn’t this have been a question that almost every student answered correctly?

The next question is another that you would expect every beginning Algebra student to understand.

simple algebra 1 question

The students did not even have to solve for “n” in this question if they forgot how.  All they had to do was plug the multiple choice answers for “n” into the equation and see which one satisfied the limitations of the equation.

The next question is the only relatively difficult sample question in my opinion.  Nonetheless, it is probably more difficult for an adult who has not had Geometry in over 30 years than a student who has recently completed a Geometry course.

rectangle area question

rectangle area answer

I teased the formulas needed to solve this problem from my memory.  To be fair, I do use the ½ base x height formula to compute land areas of triangular shaped parcels as part of my job, but I did have to remember a2 + b2 = c2.  Drill and skill at its finest!  Astonishingly, only 25% of students, most of them fresh out of Geometry (only 7% of students had NOT taken Geometry), answered this correctly.  As far as Geometry questions go, this is not even a particularly difficult one except that it was not multiple choice.  The solution actually required students to know how to compute an answer on their own.  It was also the sample question on which the students performed the most poorly.  This is not surprising given how today’s education philosophy puts so little value on practice and so much on group work and “theory”.

I want to add one final comparison that I think truly highlights the problems with our education system.  Surprisingly, or maybe not, Asian Americans are not highlighted as a subgroup in the reports put out by the NCES.  The data is there, just like it is for Blacks and Hispanics and Whites, but it is just…ignored.  Let’s take a look at how Asian Americans perform.  Reading first.

9-year-olds

asian scores read 9

13-year-olds

asian scores read 13

17-year-olds

asian scores read 17

Next, Math

9-year-olds

asian math scores 9

13-year-olds

asian math scores 13

17-year-olds

asian math scores 17

Asian Americans have higher scores at every age group in both reading and math.  I do not believe that Asian Americans are inherently smarter than every other sub-group, rather the Asian American family makes education a priority.  They also put less stress on the effort and more on the achievement.  They value practice and mastery.  They do not abide failure and they tend to limit their children’s extracurricular activities.  In short, they are the perfect match for an education curriculum that expects mastery to occur at home and for parents to be the means to this end.

But even if I have over simplified the Asian American dynamic, if it was all about ethnicity or even wealth (Asian Americans have one of the highest income levels as a subgroup), we could expect Asian Americans to perform as well as Asians in other countries on the PISA tests, but that has not happened.  They DO score higher than every other American subgroup on the international test, but they still score below other Asian nations, as can be seen in the following charts.

asian pisa 2012

all pisa 2012 chart

In conclusion, in light of the number of years educators and curriculum have had to raise test scores, the amount of money spent on education, and the number of years we have tread water in the status quo,  very little progress has been made based on the NAEP Long Term test scores.  While this alone might not be cause for concern,  though I can hardly imagine why not, when these results are considered in light of students’ performance on international tests and their diminished preparedness for college, there is no mystery as to why parents, politicians, professors, and even many educators have reached the end of their patience.  Anti-education reformers can waste all their time trying to convince the public that things are fine with anemic NAEP score gains and by pointing to poverty and high stakes testing, but they run the real risk of destroying the very institution they are trying to protect through their arrogance and condescension.  If that sounds harsh, I am sorry, but I will not buy into the argument that U.S. education is fine outside of the inner-cities and could be miraculously cured if we throw more money at it.  If that is to be your rhetoric, your position, your crutch, then we have very little to discuss and I pity the children being forced to learn in these institutions, especially disadvantaged children.