A Tale Told by an Idiot, Dept.

Yet another article on Singapore Math, which in the end signifies nothing. In fact, this one could probably be used as a template for so-called education reporters when they write about math education.

It starts out well enough with a very concise history of the program that was developed in Singapore:

What is referred to as Singapore Math in other countries is, for Singapore, simply math. The program was developed under the supervision of the Singaporean Minister of Education and introduced as the Primary Mathematics Series in 1982. For close to 20 years, this program remained the only series used in Singaporean classrooms.

In fact, the “Primary Math” series is simple and effective and has been used by many homeschoolers in the US for many years.  Some mathematicians (Richard Askey from U of Wisconsin among them) revamped the series for use in U.S. classrooms so that it used U.S. currency and English system measures (in addition to the metric system). It was called Primary Math, U.S. edition.

Over the years, the Primary Math series in Singapore was replaced by “new and improved” versions that in the opinion of many users of the original series, was watered down and prone to some of the U.S. reform ideas, such as increased use of calculators. Nevertheless, enough of the main tenets of the original Primary math series have remained in the subsequent editions so that the textbooks still stand out.

The article leads with this precis of the framework of Singapore Math:

The framework of Singapore Math is developed around the idea that learning to problem-solve and develop mathematical thinking are the key factors in being successful in math.

Ignoring for the moment the trendy use of “problem-solve” as a verb (instead of saying “learning to solve problems”), the above intro is not bad unto itself. But, not to disappoint, things go predictably downhill with the analysis of “pros and cons” of Singapore Math.

Actually the listing of the “pros” of Singapore Math are not bad; hard to disagree with these, for example:

  • Textbooks and workbooks are simple to read with concise graphics.
  • Textbooks are sequential, building on previously learned concepts and skills, which offers the opportunity for learning acceleration without the need for supplemental work.

But then we have the obligatory “not like traditional math” narrative:

  • Asks for students to build meaning to learn concepts and skills, as opposed to rote memorization of rules and formulas.

Yes, it does require students to learn concepts and skills and provides a contextual background for how the rules work. But so did many textbooks of the past which I’ve talked about extensively.  And it isn’t like teachers don’t teach the conceptual underpinnings.  Caricaturizing traditional math approaches as “rote” never gets old, though, as the writer of the article shows.

But moving on to the “cons” of Singapore Math, things get really interesting.  We start with “Requires extensive and ongoing teacher training, which is neither financially or practically feasible in a number of school districts.”

Yes, it does require some teacher training, but if you’re going to complain about financial burdens and practical feasibility, why not take a look at the Professional Development (PD) seminars teachers are forced to attend to learn the “Common Core way” and other topics.  For example, I was asked to attend six off-site workshops to “collaborate” with other math teachers in the county in order to learn innovative approaches to achieve the Common Core’s “Standards of Mathematical Practices (SMPs)”.  Aside from the impracticality of missing six days of instruction time, there was also the financial burden of hiring a sub for me for six days.  Then there was also the PD itself which was all trendy talk about how math has been about “answer getting” when the process is key and other balderdash that passes as educational wisdom while padding someone’s resume.

Then there’s this:

  • Less of a focus on applied mathematics than traditional U.S. math textbooks. For instance, the Everyday Mathematics program emphasizes data analysis using real-life, multiple step math problems, while Singapore Math’s approach is more ideological.

Less focus on applied math than traditional textbooks? Really?  Primary math is all about applied math, but the term “applied math” has a different meaning when talking about math education these days. It used to be we could talk about students learning to solve problems.  But “solving problems” in today’s edu-lexicon means the standard one-answer, non-open-ended type of problems (like “Johnny had 5 apples and gave some away. He has three apples left. How many did he give away?”) which is viewed as “dull, boring and deemed to not imbue students with a problem solving “schema”.  Furthermore, the problems are viewed as contrived, and not something they would use in “real life” (even though they are very applicable to real life).

Actually, Singapore Math provides challenging multi-step problems which enable students to generalize problem-solving procedures to solve a variety of different problems.  But the author would rather compare Singapore Math to Everyday Mathematics whose “discovery” and “spiral” approach provides little to no background in how to solve much of anything.  See this article to get an inkling or talk to any parent whose child has had to endure Everyday Math.) Apparently, Everyday Math is now incorporating “data analysis” to go along with the latest shiny new trend to teach statistical concepts in K-6.

What the author means by Singapore’s approach being more “ideological” is anyone’s guess, but it presents a damned-if-you-do, and damned-if-you-don’t mentality. On the one hand, presenting problems that involve computation is held in disdain because it doesn’t present the real beauty of math. But then there are complaints that math is presented as too abstract (a complaint generally leveled at algebra courses) and the reason students don’t like it is because it isn’t relevant.  So I guess data analysis is the new middle ground–everybody is happy learning about frequency histograms, box and whisker plots, and mean absolute deviations in the sixth grade.

Finally there is this:

Doesn’t work well for a nomadic student population. Many students move in and out of school districts, which isn’t a big problem when the math programs are similar. However, since Singapore Math is so sequential and doesn’t re-teach concepts or skills, using the program may set these students up for failure, whether they’re moving into or out of a district using it.

Apparently, the author of the article and many others believe the premise upon which Common Core was sold: i..e., that the U.S. student population is largely nomadic with huge movement into and out of states and school districts on a constant basis.  This belief persists despite evidence to the contrary obtained by a glance at U.S. Census data.  And even if it were the case that the U.S. is nomadic, that shouldn’t be a problem since there are now Common Core aligned Singapore Math books which teach to the same standards as all the other states.  Of particular interest, however, is the statement that “Singapore Math is so sequential and doesn’t re-teach concepts or skills.”  Actually, it does–it just takes up where it left off in the previous grade, like most textbooks do.  Maybe it doesn’t spend as much time with review as others, but one can always build in reviews as needed.

But finding problems where none exist is the bread and butter of many edu-writers these days.  And unfortunately, ignoring the real problems that accompany many of the student-centered, inquiry-based approaches that are increasingly popular in K-6 is another.




Skin Deep Understanding, Dept.

Ed Week, the self-professed “newspaper of record in education” does it again, with an article on San Francisco’s decision to do away with algebra in the 8th grade.  The article does everything but post banners and host a confetti parade for such decision, but is also careful to provide “nuance” and the semblance of balanced reporting.

The article sets the stage and tone of San Francisco’s decision and what it meant:

That means no “honors” classes. No gifted track. No weighted GPAs until later in high school. No 8th grade Algebra 1. In terms of curriculum, this is about as controversial as it gets. And that’s not just because of its math implications, but because of the parental pushback such a plan is guaranteed to generate. In effect, by de-tracking math classes, San Francisco has done away with one of the key avenues that the well-connected use to give their children an academic advantage.

That last sentence should win an award.  It’s all about equity, and algebra in 8th grade was inequitable because it benefitted the well-connected.  These same “well-connected” families shell out money for tutoring and learning centers to make up for what their children are not being taught in the earlier grades. I guess it’s “shame on them” time, and the Ed Week definition of equity is therefore to lower the tide for all.  And of course no mention of the non-well-connected families who might have benefitted from algebra in 8th grade.  That might be too “nuanced” an argument.

No, much better to rely on the tried and true messages:

Federal data show that white and Asian students disproportionately take Algebra 1—long seen as a critical gateway to advanced math—before high school, while African-American and Latino students are overrepresented among those taking it for the first time in grade 9. Many of them take it as late as their junior or senior year.

And then, of course, to accompany it with a chart showing –goodness–that the repeat rates for algebra 1 for all ethnic groups declined dramatically since the enactment of the ban on algebra1 in 8th grade.

Very impressive.  It brings to mind a question though.  How is algebra 1 taught in high school now?  And I almost hate to phrase it in this un-nuanced way, but is it “watered/dumbed down?”

I bring this up because of how they present the “before” picture, showing two contrasting  (i.e., “nuanced”) views (they even use the word “nuance” here) thus doing a good job of appearing to be balanced:

Research paints a far more nuanced picture than either side in such debates typically acknowledge. For the average student, researchers say, early exposure to a challenging class like algebra probably does pay off.

But in a 2015 study, the University of North Carolina’s Thurston Domina and colleagues tracked how California’s uneven 8th grade algebra-for-all rollout played out across districts. In a surprise finding, they discovered that higher enrollments in early algebra were linked to a decline in students’ scores on a state math test.

“I think the failure of 8th grade algebra was one of just not preparing teachers and school leaders to understand the policy and to implement it well,” said Domina, an associate professor of education policy and sociology. “The whole idea was to have heterogeneous, rigorous classes, and schools didn’t have the capacity to pull that off.”

The article then talks about “instruction vs textbook” and how important the method of instruction is in all this.

As for implementation, San Francisco administrators have shaped day-to-day teaching and curriculum to support the district’s focus on equity. Heavily based on work by Jo Boaler, a Stanford University professor of math education, the curriculum emphasizes having groups of students work through a series of ambitious math tasks.

Traditional math teaching, the thinking goes, tends to reinforce rather than break down inequities.

“If you have a procedural textbook, not only is there nothing to collaborate about, the ‘smart kid’ in the group is always the one who gets the computation right,” said Lizzy Hull Barnes, the mathematics supervisor for the San Francisco district. But when students wrestle over problems together, they can use different methods, compare approaches, and figure out why some work and others don’t, making all of them active participants in the learning, she said.

Jo Boaler’s methods seem to be accepted by Ed Week and other education reporters as beyond reproach. She claims her methods are backed by cognitive science research, making claims such as “making mistakes makes your brain grow”.  Though in all honesty, since she was challenged by scientific-minded people on such statement, there is now a more “nuanced” version of said statement. Nevertheless, “getting the right answer” is now symptomatic of “procedural” instruction and making mistakes is the watchword for ensuring “deep understanding” in this brave new world of math education.

Collaboration is key to 21st Century learning. Without it, you’re simply doing procedural stuff and “answer getting” which is stated with references to dubious research that show that such approaches have failed thousands of students.  “Procedural textbooks” are assumed to provide no pathways to understanding; it’s all rote memorization, unconnected ideas and bags of tricks.  No one in these types of articles ever asks parents of students who make it into STEM fields what these students do to gain mastery of the content. It’s simply assumed that such students are gifted, or highly intelligent, and are destined to understand no matter how the material is presented.

Well, the article does hint at this.  It admits that there are some students who have taken algebra elsewhere–and that this poses a problem in student-centered, inquiry-based, collaborative classrooms.

Most teachers praise the social-justice impetus behind the math plan. But they also say that heterogeneous classes pose unique problems.

Students bring vast achievement differences to class, a situation that’s not helped by ambitious parents who, now, shell out thousands of dollars for students to take non-district algebra classes over the summer in the hopes of getting their children into geometry early.

“We have kids who have seen some of the math before. Their knowledge may not be deep, it may be procedural, but they come in thinking, ‘I know this already.’ You have to authentically challenge them, too,” said Daniel Yamamoto, an algebra teacher and the math-department chairman at Burton High. “And there are other kids who say [in response], ‘I have nothing I can add to this discussion.’ “

And there you have it: Procedural knowledge is never “deep”.  It goes without saying, I guess, which would explain why our reporter didn’t question such statement. It would be nice to get interviews with some of the teachers who disagree with the statements above, rather than just relying on a statement that “most teachers praise” the this and that of banning algebra in 8th grade and about the false dichotomy between procedures and “deep” understanding. Or course, not too many of those teachers want to be interviewed for fear of appearing on record–and possibly losing their jobs.

Interesting that Phil Daro, one of the authors of the Common Core math standards and the person who holds “answer getting” in disdain, is hedging his bets on the algebra in 8th grade question.  On the one hand, the article shows he was instrumental in San Francisco’s decision:

“Tracking is an evil. But fear of tracking is a problem, because you do have to talk about differences in students’ backgrounds,” said Phil Daro, a common-core-math writer who helped San Francisco design the new course sequence.

But then it goes on to say:

“[H]e continues to worry that San Francisco leaders’ decision four years ago not to offer a limited amount of Algebra 1 in 8th grade might someday backfire. “I thought politically it was a mistake,” he said. “It may still turn out to be one.”

Oh, and here’s some balanced reporting, way at the end:

District leaders, for their part, are focused on more immediate concerns. Asked what challenges remain, Barnes points to the progress of black students as an area in which the city needs to double down. Those students have gained in math and science credits, alongside their peers, but those gains aren’t yet showing up on state test scores or in enrollments in AP Calculus.

Ah ha!  Interesting.  So maybe it isn’t working after all! But wait; there’s this:

Her colleague Angela Torres, a math-content specialist, cites the difficulty in ensuring that all teachers feel confident in the new curriculum and teaching methods.

Right. Always leave room in politics and in reporting for blaming it on the teachers who just aren’t doing reform math correctly.

Brave New World of Education Reporting, Dept.

I should go easy on this article because it’s written by a student from the School of Journalism at Michigan State University.  Nevertheless, since education writing is usually about agreeing with those who advocate for ineffective practices, with little or no investigation of the other side, this article is emblematic of how reporters are trained in education writing.

We start with the standard quote from a teacher about how it used to be and how it is now:

Mindy Willis, a curriculum consultant for Pinckney Community Schools, says the role of a teacher is evolving. When she was in grade school, the teacher taught in a direct manner, the students took notes and then were later tested on it, but she says that’s not how the classroom looks now. Today, teachers are managing their classrooms in what’s called an inquiry-based instruction.

“With inquiry-based instruction, you design learning for students where they’re actually going through a process of figuring things out themselves,” said Willis. “So basically, the kids are constructing their own knowledge based on experiences that they’re having and they’re driving, and the teacher is a facilitator to guide them through that process as opposed to just spitting it at them and then regurgitating that information.”

Notice that the “how we teach now” is contrasted with past practices by denigrating them: e.g., teachers “spitting” information at students who then “regurgitate” the information.  Such mischaracterization is a key feature of education reporting and it looks like MSU’s School of Journalism is leading the way.

There’s even a table comparing how it used to be to what we’re moving toward:

There’s plenty to notice in this table, but one thing that grabbed my eye was the description in the “Moving from” column regarding lesson structure: “Lessons contain low-level content, concepts mentioned; lessons not coherently organized.”  I’ve gone through many older math textbooks and do not agree with the caricature presented.  Topics are presented and built upon in a very coherent fashion.  One has only to look at some of today’s modern “spiral process” textbooks (e.g., Everyday Math; Investigations in Number, Data and Space) to see that lessons are anything but coherent.  And in the “Moving toward” column, we see that lessons focus on “high-level and basic” content.  Hard to know how you can do both at the same time, but what I think they mean is they present a “top down” approach, with concept first, and procedure last–and no teaching the procedure until students “understand” the conceptual underpinning. And needless to say, but I’ll say it, such approach has had disastrous results.

And of course no story on education would be complete without talking about project-based learning. This article does not disappoint in that regard:

Another widespread idea across the country is project based learning. According to the Buck Institute for Education, project based learning is about students creating projects that solve real world problems, then students present their finished project to an audience. By doing this repeatedly, students learn key skills like critical thinking, communication, collaboration and creativity.

Yes, the 4C’s: Critical thinking, communication, collaboration and creativity.  Why bother with learning what they need to know in order to do a project–they learn it on the job in a “just in time” manner.  And in so doing, learn the 4C’s which are more important than content knowledge.

The authors of this article even cite research that supports the idea that such skills are key for students to succeed in the 21st Century.

In a research study conducted by the Buck Institute for Education that compared various organizations to their opinions on “21st century skills,” most organizations found critical thinking, collaboration and communication as extremely important attributes in an employee. You can access their research in the link here.

Of course, content knowledge is important–for the teacher, that is:

“A lot of people don’t realize just how much content area preparation secondary teachers have to go through to get their degrees, to become certified and to become teachers,” says Bieda.

Well, it’s good that somebody knows the content. I wonder how the teachers obtained that contact. Through direct instruction or Project Based Learning?  In any event, that content is being kept a deep dark secret and providing students such information would be “spitting it at them” only to have them “regurgitate it back”.  And we can’t have that.  Because the new method is working just great isn’t it?

Don’t hold your breath, by the way, for a follow-up story of how students who wind up majoring in STEM fields are getting the education they need.

Stop Me If You’ve Heard This, Dept.

This article talks about a book titled “Systems for Instructional Improvement”   coauthored by the dean of the University of Southern California ed school.  It is described as  “dedicated to improving math instruction in the U.S.”

Why is it that just about every book, article, tweet, and Linked-In polemic that purports to put math education back on track starts from the following assumption:

“For the past 25 years or so, there’s been a growing recognition that students at the middle-school level, in particular, aren’t developing a deep understanding of mathematics,” said Thomas Smith, dean of UC Riverside’s Graduate School of Education. “A big piece of that is because of the way students in the U.S. are taught; current math instruction tends to be highly procedural — as in ‘use these steps to solve these types of problems’ — instead of allowing students to investigate real-life problems and experiment with different types of solution strategies.”

The same catchwords end up in this catechism of edu-wisdom: “Deep understanding of mathematics”.  Just how deep of an understanding of math do you want middle school students to have? Even in freshman calculus courses, students learn a short-cut version of what limits and continuity are in order to get to the powerful applications of same; namely derivatives and integrals and the (yes) procedures for taking derivatives and finding anti-derivatives.

Students who go further in math will master the delta-epsilon definitions of limits and continuity, and learn about least upper bounds, greatest lower bounds,  limit points, cluster points, open and closed sets and compactness. Such deep understanding of calculus is largely inappropriate at the freshman level–one has to start somewhere in order to go deeper. And so it is the same with middle school math. One starts with procedures and in subsequent math courses, one goes deeper.

And it isn’t as if teachers and textbooks have not provided the conceptual understanding that underlie the procedures that math reformers seem to find so “rote like”. It’s just that students like to know how to do things and as has been stated in various research studies, procedural fluency and understanding often work in tandem. Sometimes conceptual understanding comes first, and sometimes the procedural understanding. But there is a stated resistance to learning the procedure first as if it is handing it to the student and taking the easy way out.  Teachers are made to feel guilty when, seeing that their students are unable to solve the problems assigned, take to breaking down the procedures step by step.

Also, the problems that middle school students have had to solve over the years are really not as far-removed from reality as the spin-meisters would have us believe. K-8 math is largely “applied math” and in earlier times was an essential part of everyday life.  A glance at the textbooks used in Singapore (the Primary Math series is a good example) has very straightforward problems that allow students to apply the concepts of things like decimal, fraction and percent operations.  An example:  “Alex spent 1/3 of his pocket money on a toy airplane and 2/3 of the remainder on a toy robot. He had $20 left.  How much did he spend altogether?”

Singapore has boasted high scores on international tests for years, but the problems that students solve there may be held in disdain by math reform types. Perhaps they think they are not relevant to students concerns. If students are not given proper instruction on how to solve such problems, and are expected to discover “strategies” for solving, they will tend to ask “When am I ever going to use this in real life?”   If given proper instruction with scaffolded problems that are variations on the initial worked example, students generally will tackle such problems. The “When will I ever use this” question is generally an expression of frustration.

Math reformers want kids to use elaborate techniques to get simple answers and call that “understanding”. Or even “deep understanding”.  What they think is understanding is visualization which is not what mathematicians mean by understanding.

But the standard talking points that pervade books about education continue.  The article ends with this chestnut:

“When it comes to teaching, people are often wedded to the ways from which they learned,” Smith added. “But the reality is those ways don’t always help all students learn. Our goal is to support teachers and coaches, as well as school and district leaders, to improve teaching and learning for all students.”

Interestingly, over the past 30 years, math has been increasingly taught in the manner these reformers want to see it done (in the lower grades primarily).  If you point this out to them, they will generally say one of two statements: “No, that isn’t true, but I wish it were” or “They aren’t doing reform correctly.”

In the meantime, many books like “Systems for Instructional Improvement” have been written and not much has changed.  Oh, right. It’s because they aren’t implementing the recommendations. Or they’re doing them wrong.  Or (insert your own excuse here _________________).