Significance of PISA math results

A new round of two international comparisons of student mathematics performance came out recently and there was a lot of interest because the reports were almost simultaneous, TIMSS[1] in late November 2016 and PISA[2] just a week later. They are often reported as 2015 instead of 2016 because the data collection for each was in late 2015 that would seem to improve the comparison even more. In fact, no comparison is appropriate; they are completely different instruments and, between them, the TIMSS is the one that should be of more concern to educators. Perhaps surprising and with great room for improvement, the US performance is not as dire as the PISA results would imply. By contrast, Finland continues to demonstrate that its internationally recognized record of PISA-proven success in mathematics education – with its widely applauded, student-friendly approach – is completely misinforming.

In spite of the popular press and mathematics education folklore, Finland’s performance has been known to be overrated since PISA first came out as documented by an open letter[3] written by the president of the Finnish Mathematical Society and cosigned by many mathematicians and experts in other math-based disciplines:

“The PISA survey tells only a partial truth of Finnish children’s mathematical skills” “in fact the mathematical knowledge of new students has declined dramatically”

This letter links to a description[4] of the most fundamental problem that directly involves elementary mathematics education:

“Severe shortcomings in Finnish mathematics skills” “If one does not know how to handle fractions, one is not able to know algebra”

The previous TIMSS had the 4th grade performance of Finland as a bit above that of the US but well behind by 8th. In the new report, it has slipped below the US at 4th and did not even submit itself to be assessed at 8th much less the Advanced level. Similar remarks apply to another country often recognized for its student-friendly mathematics education, the Netherlands, home of the PISA at the Freudenthal Institute. This decline was recognized in the TIMSS summary of student performance[1]with the comparative grade-level rankings as Exhibits 1.1 and 1.2 with the Advanced[5] as Exhibit M1.1:

pastedimageBy contrast, PISA[2] came out a week later and…

Netherlands 11
Finland 13
United States 41

Note: These include China* (just below Japan) of 3 provinces, not the country – if omitted, subtract 1.

Why the difference? The problem is that PISA was never for “school mathematics” but for all 15-year-old students in regard to their “mathematics literacy[6]”, not even mathematics at the algebra level needed for non-remedial admission to college much less the TIMSS Advanced level interpreted as AP or IB Calculus in the US:

“PISA is the U.S. source for internationally comparative information on the mathematical and scientific literacy of students in the upper grades at an age that, for most countries, is near the end of compulsory schooling. The objective of PISA is to measure the “yield” of education systems, or what skills and competencies students have acquired and can apply in these subjects to real-world contexts by age 15. The literacy concept emphasizes the mastery of processes, understanding of concepts, and application of knowledge and functioning in various situations within domains. By focusing on literacy, PISA draws not only from school curricula but also from learning that may occur outside of school.”

Historically relevant is the fact that conception of PISA at the Freudenthal Institute in the Netherlands included heavy guidance from Thomas Romberg of the University of Wisconsin’s WCER and the original creator of the middle school math ed curriculum MiC, Mathematics in Context. Its underlying philosophy is exactly that of PISA, the study of mathematics through everyday applications that do not require the development of the more sophisticated mathematics that opens the doors for deeper study in mathematics; i.e., all mildly sophisticated math-based career opportunities, so-called STEM careers. In point of fact, the arithmetic of the PISA applications is calculator-friendly so even elementary arithmetic through ordinary fractions – so necessary for eventual algebra – need not be developed to score well.


[2] (Table 3, page 23)
[5] [Distribution of Advanced Mathematics Achievement]

Wayne Bishop, PhD
Professor of Mathematics, Emeritus
California State University, LA

Significance of PISA math results was originally published on Nonpartisan Education Blog

Significance of PISA math results was originally published on Nonpartisan Education Blog

Wayne Bishop’s observations on the Aspen Ideas Festival session, “Is Math Important?”

Editors’ Note:

David Leonhardt is Washington Bureau Chief for the New York Times, won a Pulitzer Prize for his reporting on economic issues, and majored in applied mathematics as an undergraduate at Yale. Mr. Leonhardt chaired the panel, “Deep Dive: Is Math Important?” an “event” in the program track “The Beauty of Mathematics”. Other program track events included individual lectures from each of the panelists.

Mathematicians might consider the panel composition rather odd, and ideologically one-sided. Three panelists are not mathematicians, but are wholehearted believers in constructivist approaches to math education, often derided as “fuzzy math”. Two of them claim, ludicrously, that high-achieving East Asian countries teach math their way. The aforementioned panelists are: journalist Elizabeth Green, education professor Jo Boaler, and College Board’s David Coleman, with a degree in English lit and classical philosophy. When only one side is allowed to talk, of course, it can make any claims it likes.

Watch for yourself: Aspen Ideas Festival: Deep Dive: Is Math Important?

Professor Bishop’s essay, written in the form of a letter to David Leonhardt, can be found here.


Wayne Bishop’s observations on the Aspen Ideas Festival session, “Is Math Important?” was originally published on Nonpartisan Education Blog

Wayne Bishop’s Response to Ratner and Wu (Wall Street Journal)

Making Math Education Even Worse, by Marina Ratner,

Dear Hung-Hsi,

It pains me to write but in spite of all of your precollegiate mathematics education knowledge and contributions, Prof. Ratner got it right and you “missed the boat” in response:
The CA Math Content Standards were – and still are – the best in the country. They have problems; e.g., there is too much specialized focus in its thread on Statistics, Data Analysis, and Probability and, even worse, Mathematical Reasoning. No sensible person can be against mathematical reasoning, of course, but that is exactly the point. Sensible people embed it everywhere and, as a standalone item, it becomes almost meaningless – hence the paucity (as in none) of CA Key Standards in that category. The writers included it to help ensure Board of Ed approval because most professional math educators were strongly objecting to the entire Stanford approach. Perhaps the most egregious, is your characterization of California’s problems using poison words: “rote-learning of linear equations by not preparing students for the correct definition of slope.” This is at best misleading and closer to being flat wrong:
From the introduction to Grade 7:
“They graph linear functions and understand the idea of slope and its relation to ratio.”
This is followed specifically with two Key Standards and examples:
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the ratio of the quantities.
In what way(s) do you find the relevant 8th grade standard in the CCSS-M, Expressions and Equations (EE.8 #5,6), to be conceptually superior? (The word is used once in the intro to Grade 7 but it is not mentioned thereafter.) Formally proving that all pairs of distinct points determine similar triangles so that this ratio is well-defined would be mathematically necessary to be completely logical but I doubt if that’s what you meant particularly since traditional proof has been downplayed so badly even in the high school CCSS-M, much less 8th grade, especially in comparison with the CA Math Content Standards.

Regarding the general concept of competent Algebra 1 (not some pretense thereof), it was, it is, and it will remain standard in 8th grade (if not already accomplished in 7th grade) for self-respecting, academically-oriented private schools. As you well know, the Stanford Math group who wrote the CA Standards started with the egalitarian notion that this should be an opportunity for everyone including those who do not have access to such schools. It cannot be and was not intended to be just imposed that traditional Algebra 1 be the math course for all 8th graders but the group worked backwards from that target step-by-step through the grades in order to get there comfortably (such as developing the concept of slope in 7th grade that you appear to have missed). Is every detail spelled out? Of course not, nor should they be, but the key ideas – even set off as Key Standards – are there and presented considerably more clearly than in the CCSS-M.

There is statistical evidence that the goal did improve the state of mathematics competence in California, but we both know the CA Math Content Standards fell well short of the ideal. It was not – as your words could be interpreted to imply – that they reflect an inherent lack of development of student understanding. The primary villain is the overwhelming mandate for chronological grade placement (age-5) for incoming students and almost universal social promotion. Far too many students are not competent with the standards at their grade levels – sometimes years below – yet they move on anyway. Algebra in 8th grade – Algebra in 11th grade or even Algebra in college – is not realistic for all but truly gifted students who lack easily identifiable mathematics antecedents. A less common problem, but damaging to our most talented students, is the reverse situation. Advancement in grade level (as was done with my son at his private school and now chair of Chemistry and Biochemistry at Amherst College) is almost unheard of. Although mandated by many districts, and underscored by the API scoring of schools, mandating that all students be in an honest Algebra class in 8th grade without a reasonable level of competence with the Standards of earlier grades was never the intention. It was to be the opportunity, not the mandate.

“Moreover, Common Core does not place a ceiling on achievement. What the standards do provide are key stepping stones to higher-level math such as trigonometry, calculus and beyond.”

Although these words are regularly repeated, reality is the diametric opposite. Across California, CPM (supposedly, College Preparatory Mathematics) is back with a vengeance. Ironically, it was the very catalyst that spawned the now defunct Mathematically Correct and it pulled its submission to California from the 2001 approval process rather than be rejected by our CRP (Content Review Panel). You’ll recall that it and San Francisco State’s IMP were among the federally blessed “Exemplary” programs for which the only mathematician, UT-SA’s Manuel P. Berriozábal, refused to sign off. Weren’t you among the signatories of David Klein’s full-page letter of objection in the Washington Post? One of CPM’s long-standing goals is to have ALL assessments – even final examinations – done collectively with one’s assigned group. It makes for a wonderful ruse – all students can appear to be meeting the “standards” of the course (even if absent!) – while deeply frustrating those students who are “getting it” (often with direct instruction by some family member who knows the subject). Trigonometry, calculus, and beyond from any of CPM, IMP, Core-Plus (all self-blessed as CCSS-M compatible)? It just doesn’t happen. However, from the homepage of Core-Plus:

“The new Common Core State Standards (CCSS) edition of Core-Plus Mathematics builds on the strengths of previous editions that were cited as Exemplary by the U.S. Department of Education Expert Panel on Mathematics and Science”

What did happen – may already be happening again? Beneath the horizon, schools began to offer a traditional alternative to provide an opportunity for adequate preparation for knowledgeable students with math-based career aspirations. What also happened (but may not be successful this time because of the SBAC or PARCC state examinations?) was that other students and their parents petitioned their Boards of Education for an elective choice and, if unfettered choice was granted, the death knell sounded on the innovative “deeper understanding” curriculum and pedagogy.

Finally, you do acknowledge the ridiculous nature of the 6th grade “picture-drawing frenzy” observed by Prof. Ratner but seem to imply it was an isolated incident instead of her description, “this model-drawing mania went on in my grandson’s class for the entire year.” The fact is that such mis-interpretations of “teaching for deeper understanding” are going on for entire years in classrooms – in entire districts – all across the country; they are even taught by professional math educators as mandated by Common Core. You described her observation as a “failure to properly implement Common Core” and I am sure that you believe that to be the case but your conviction is belied by the fact that one of the three primary writers of the CCSS-M and the head of the SBAC-M is Phil Daro (bachelors degree in English Lit). Phil Daro has been strongly influential in precollegiate mathematics education – curricula and pedagogy – across California for decades, my first working acquaintance with him was in 1988, months prior to the first NCTM Standards. His vision for the “right” way to conduct mathematics classrooms (not “to teach”) helped lead to the 1992 CA Math Framework, MathLand-type curricula, and the ensuing California battles of the Math Wars with our temporary respite beginning in late 1997. Unfortunately, his vision is not only reinvigorated here in California, it is now a huge national problem and Prof. Ratner “nailed it”.

Wayne Bishop

Wayne Bishop’s Response to Ratner and Wu (Wall Street Journal) was originally published on Nonpartisan Education Blog

Wayne Bishop’s Response to Ratner and Wu (Wall Street Journal) was originally published on Nonpartisan Education Blog

Wayne Bishop’s Response to Ratner and Wu (Wall Street Journal) was originally published on Nonpartisan Education Blog