How’s It Been Working So Far? Dept.

NSF never ceases to fund questionable math ed practices. Now they’ve given \$1.5 million to University of Washington to devise ways to introduce mathematical modeling in elementary school.

“Very little has been done to find the best approaches for introducing mathematical modeling at the elementary school level,” said Aguirre. “What we’re trying to do is lay a basic foundation for developing an elementary curriculum around mathematical modeling and providing resources to educators.”

As an example of the type of problem we’re talking about:

“Here is a traditional mathematics problem that elementary students might typically encounter: 24 students are going on a week-long camping trip. Each student receives three healthy meals each day. How many healthy meals are needed for the camping trip?”

NOTE: This is obviously supposed to be inferior. Here’s their superior approach:

” “An approach based on mathematical modeling first introduces the situation to students: ‘How much food do we need to bring on this trip?’” said Aguirre. That lack of structure allows students to come up with their own process to address this situation.” “

Yes, lack of structure and ill-posed problems are really what kids need in elementary school. Given that they aren’t being taught standard algorithms until 4th, 5th and 6th grade thanks to liberal interpretations of Common Core (that by the way lend themselves to such liberal interpretations), this will be the icing on the cake that everyone has been waiting for.

This is consistent with the math reform approach which is to present students with a steady diet of “challenging problems” that neither connect with the students’ lessons and instruction nor develop any identifiable or transferrable skills.

The following problem which I saw in a study that I had to read in ed school is similar to the one above: How many boxes would be needed to pack and ship one million books collected in a school-based book drive? In this problem the size of the books is unknown and varied, and the size of the boxes is not stated. While some teachers consider the open-ended nature of the problem to be deep, rich, and unique, students will generally lack the skills required to solve such a problem, skills such as knowledge of proper experimental approaches, systematic and random errors, organizational skills, and validation and verification.

Oh WAIT, I have it wrong. With this NSF grant, they’ll be able to teach elementary students all of those skills necessary. My bad!

Articles I Never Finished Reading, Dept.

“We need to move away from classrooms that have not progressed since the days of chalk and talk – with a desk at the front, where teaching remains in the hands of teachers and students are passive recipients of information, rather than active learners.

Similarly, subject faculties are often entirely separate entities, dividing the chefs from the software developers, so never the twain shall meet.

This traditional scenario simply doesn’t represent the workplace that our students will enter – the old-style office is just as last century as the classroom. In the future, chefs will probably need to work hand-in-hand with software developers to create apps to promote their restaurant or hire a social media expert to help them develop their advertising strategy.”

First of all, he’s making his point via something that people are reading, thus using direct instruction. So he’s doing his own version of chalk and talk as do many ed school teachers, and professional development vendors. He also assumes that no “aha” moments can come from direct instruction, and that such mode consists entirely of lecture, with no questions or Socratic type dialogue from the teacher.

Putting that aside for the moment, let’s look at his vision of the future. Most professionals already have developed their level of expertise and are no longer novices, as most schoolchildren are. They can thus interact in ways that those still learning the basics cannot. But this doesn’t bother him. In his view, we can all meld history with math with art and spelling and tear down what he feels are the restrictive borders of education.

Such Summerhillian vision might appeal to those in their twenties who hold to such ideals, but I’m reminded of a story my uncle once told me. In the days of newsreels (before television), there was once a feature he saw about what the future would look like. Airplanes were increasingly being used for commercial purposes, so this newsreel “look into the future” talked about how “icemen” (people who delivered ice to your home to use in ice-boxes which were the way house refrigerators worked back then) would be phased out as airplanes would drop blocks of ice on your front porch.

While the reality of dropping heavy items on residential property escaped the creators of this feature, so did the possibility that something other than ice could be used as a refrigerant.

In the meantime, fundamental knowledge is not going to disappear to be replaced by Google, or Siri. But don’t tell the author about this.

A few posts ago, I talked about how the growth in tutors and learning centers in the U.S. might be evidence that the progressive approaches to math education might not be as effective as they are touted to be.  A parallel situation exists in Canada, notably in the Alberta Province where parents have been fighting the infestation of discovery math for the past four or five years.

David Staples, a reporter, has written about the Alberta situation for years, and his latest in the Calgary Herald points up the increase in tutors and learning centers in that region:

Desperate Alberta parents are now seeing the need for private tutoring. For example, there’s been a stampede to private Kumon math and English tutoring.

There were 4,069 students enrolled in Kumon in Alberta in 2006. By 2012, there were 5,495. Then came news of Alberta’s disastrous results in math on 2013 international PISA testing, which saw a doubling of our rate of math illiterate students from 7.4 to 15.1 per cent in less than a decade. There are now 9,439 kids enrolled in Kumon. Students there attempt to learn the basic skills that many of our schools have downplayed.

This is an educational disaster, with our most vulnerable students hammered hardest, but not once have discovery math’s architects — an army of “21st-century learning” educational consultants, professors and gurus — been held to account.

The results, says Staples, is a two-tiered system of haves and have-nots.  Parents who can afford it, send their kids to private schools, enroll their kids in learning centers, or hire tutors.  Not stated, is that private schools, tutors and learning centers are likely not using the discovery methods, teacher as facilitator, or following the edicts of an  army of “21st-century learning” educational consultants, professors and gurus.

This is Rich, Dept.

NSF has doled out grant money once more in their never-ending quest to improve mathematics in middle school:

“The National Science Foundation has awarded a \$1,090,283 grant to researchers at the University of Arkansas, Brigham Young University, the University of Nevada-Las Vegas, and Grand Valley State University. The three-year grant, titled Investigating Middle Grades Mathematics Teachers’ Curricular Reasoning, will fund the work of researchers to study how middle grades mathematics teachers plan and enact mathematics lessons from a variety of resources, including textbooks and supplemental materials.

“Textbooks have traditionally driven what is learned in the mathematics classroom,” Dingman stated. “However, over the past couple of decades, and in particular since the release of the Common Core State Standards for Mathematics, we have seen more and more teachers move away from strictly following textbooks and towards using more supplemental materials that either they or someone in their district have created, or they have found online. “

I’m curious as to whether the study will find that teachers do this because textbooks are lacking in word problems that actually result in transfer to other types of problems, lacking in explanations, lacking in scaffolded problems that increase gradually in difficulty (rather than starting right off with something that causes kids to give up), and lacking in good sequencing. I’m curious also whether the study will include those teachers who use books from previous eras.

Something tells me the conclusion will be “The internet provides vast resources in math education that are not constrained by the traditional form of math teaching that currently dominate education.” In spite of the fact that the non-traditional form of math teaching has encroached upon the lower grades over the past 25 years.

The possibility of being wrong, Dept.

“Schools have to embrace a new way of teaching, he said, where learning is hands-on, extends beyond the classroom and is geared toward the needs of the individual learner.

“There is a more personal, real-world approach that defines the current edge of education reform,” he said. “It’s time for both states to move forward on this front, not double-down on a solution that was appropriate 20 years ago.”

I’ve heard this argument before. First of all, 20 years ago takes us to 1996, which is a time when NCTM’s standards were gaining a strong foothold and inquiry-based, hands-on learning was becoming a mainstay of lower grades math instruction. But ignoring that, the question in my mind is why the traditional teaching methods that were in use for many years and deemed to be appropriate are now suddenly deemed inappropriate. Is it because of the usual “Traditionally taught math never worked” trope, or are there other reasons?

Is it because we have to prepare students for jobs that haven’t been created yet? Or because everything can be answered with Google, so students have to learn how to learn rather than acquire knowledge and skills? Is it about having fun and liking math? And is the college trig class and other math requirements considered non-essential even for engineers?

Or perhaps there are other reasons often overlooked in articles such as these, and in discussions among the edu-literati. One reason why the Mass. schools outperformed others over a certain period could be because of adoption of a content-based curriculum called Core Knowledge.  The same thing happened with math in California with the 1998 curriculum which resulted in definite improvements compared to how students were performing with the 1992 framework (which drew heavily on NCTM’s standards.)  But that couldn’t be the case because everybody knows that such improvements are short-term unlike the current slew of hands-on, PBL and student-centered approaches.

You’re An Idiot, Dept.

Another article mischaracterizing the way math has been taught, as well as how it should be taught, as well as misrepresenting what Common Core requires. For starters:

“Subjects that are vibrant in the minds of experts become lifeless by the time they’re handed down to students. It’s not uncommon to hear kids in Algebra 2 ask, “When are we ever going to use this?” and for the teacher to reply, “Math teaches you how to think,” which is true — if only it were taught that way.”

I realize that my experience doesn’t count as “evidence” but when I give my algebra students the math word problems held in disdain by people like the author of this article, they are actively trying to solve them. Those that aren’t doing so need additional instruction/guidance which I provide. Students generally ask “When are we going to use this?” when they’re frustrated and don’t know how to do something, and/or because it is played up so much on TV shows and other media. Perhaps we do a disservice by saying that “you will use this later in life” because that is not necessarily true.

The author goes on:

“To say that this is now changing is to invite an eye roll. For a number of entrenched reasons, from the way teachers are trained to the difficulty of agreeing on what counts in each discipline, instruction in science and math is remarkably resistant to change.”

Interesting that he thinks math is being taught in the same old ways. Where has this author been the last 25 years with many parents complaining about the “new” ways of teaching basic arithmetic in the lower grades? It’s true that middle school and high school math have not changed too very much, except for the fact that algebra has been almost totally expunged of any kind of word problem of value, as has the requirement to do proofs in geometry. But generally, high school still offers a more traditional means of delivering instruction rather than the various pedagogical gimmicks employed in the lower grades that pass as effective practices.

Also, in articles of this type, there is no attention paid to how students who go on to STEM majors learn their math.  Many students receive help from home, from tutors, or from learning centers–something that didn’t occur that much in the days when “traditional math failed thousands of students” as the reformers like to say. It was possible for many students to make it all the way through calculus without aid of tutors or help at home–something that even today’s brightest kids are finding hard to do. Many need help in the lower grades when foundational math skills are necessary to move on.

The author goes into some history, particularly of the 60’s new math and says “Later manifestations of the impulse away from rote instruction include curricular standards created by the National Council of Teachers of Mathematics in the 1980s and the enthusiasm for “inquiry-based” science in the 1990s.”

Let me skip my usual tirade against the use of “rote instruction” as the main method by which traditionally taught math in the past is portrayed. Instead, I find it interesting that he leaves out the fact that NCTM distanced themselves from the 60’s new math when it fell out of favor, but when they came up with their infamous standards in 1989, they kept the inquiry-based practices that were being tried out in the 60’s new math. So they didn’t hate it all that much, it seems.

The article delves into how well CC approaches the concept of proportionality, and how it connects ratio to rate to proportion and ultimately slope.

“What they’re learning is: The way you find the fourth number is by setting up this gadget called a proportion,” Daro said. “That’s not really learning anything about proportionality, that’s learning how to get answers to problems in this chapter.

I’ve worked with middle school students using texts that emphasize this connection. The connection may be obvious to the teachers who have had the benefit of working with these concepts for many decades, and obvious to the authors who put together the text books. But most students want to know how to do the problems. As far as “cross multiplying”, I and others I know do teach how to calculate “the fourth number”, but in the end, the kids end up with cross multiplying because it is the way they know how to do it–and ironically, when students are coached for Math Counts competitions and standardized tests, there are short-cuts galore that they are taught.

Phil Daro, for those who don’t know the name, was the force behind the shoddy pre-1995 California standards that were responsible for atrocities like MathLand being introduced in schools, and resulting in parent outcries in areas like Palo Alto. He’s back and was one of the driving forces behind the CC math standards.

While the CC standards can be interpreted in ways that are sensible and useful, (see for example this article) one has to work to do so. One also has to ignore all the textbooks that ascribe to the reform-minded interpretations to which these standards have leant themselves.

Jumping Out of Planes Without Parachutes, Dept.

Advocates of discovery, student-centered, project-based, experiential, etc learning when told such methods are not effective react in a predictable fashion. Namely, they claim that where such methods do not work, they have been implemented incorrectly.

I have likened this response to someone upon hearing that jumping out of an airplane without a parachute results in death saying “But if you do it the right way, you can survive.”

This seems to be what’s going on in the comment section of a Huffington Post article that is non-sympathetic to “experiential learning” or “minimally guided discovery learning” or whatever it happens to be called at the moment.

The project-based learning approach, while attractive to many in the education establishment is neither necessary or sufficient. Those defending the practice seem not to care what students who are pursuing a STEM degree in a good college do to succeed. Such students do not have time for those courses, and as a friend of mine repeatedly points out: “Colleges don’t care one way or the other.”

PBL is nothing new. Kids have been doing science projects in school for years, but it was always in addition to, rather than in place of “bottom up” learning in traditional classes. Instead of devoting such approaches to after-school, they now are increasingly using up valuable class time. This has had the unintended consequence of taking up more time than normal classes, thus eating into other options like music, art, and other subjects.

From the article:

“Unfortunately, minimal guidance advocates continue to believe that too much guidance will impair later performance. They believe that the best way to make learners remember new information is to allow them to construct their own learning as opposed to being provided with a lot of facts and being made to practice basic skills. The fact that cognitive science has proved these notions false has not yet caught up with most education leaders.”