Those who read Education Week are probably familiar with the breathless reporting that Catherine Gewertz did when Common Core was being adopted by state after state. Her latest breathless report about math education is about how “talking about math” helps students learn it. Or something to that effect.

“Research suggests that when students talk more about their math thinking, they are more motivated to learn and they learn more. Talking about math thinking can also serve as a stealth form of assessment, giving teachers insight into what students have mastered and where they still need help.”

First question: What research?

Second question: Have you ever worked with middle schoolers? Articulation of what they did is not their strong suit.

Oh, you have an answer for what I just brought up? OK, let’s hear it.

“Learning to say things like, “When Robert uses this strategy, it makes me think of …” or, “This makes sense to me because … ” can help students learn how to “get mathematical ideas out into the classroom space” and build respectfully on one another’s thinking, Berry said.“

I hate to burst anyone’s bubble, but I teach middle school math. My method is to “model” articulating the structure of the problem. “Are both cars traveling the same amount of time? What can we say about the distance each car travels?” In other words getting the mathematics that matters to solving the problem “into the classroom space”. Or whatever.

“The good news, according to experts, is that math discourse is a technique that works as well virtually as it does on paper or in face-to-face classrooms. And now, when students and teachers risk feeling disconnected and adrift, there’s even more reason to consider using “math talk” techniques to help students feel engaged and see themselves—and their classmates—as valued mathematical thinkers.”

Here’s some more news, though I doubt that believers in “math talk” will find the news good. Explicit instruction in procedures and problem solving techniques, with worked examples provide students with what they need to solve problems. Expanding from a worked example to solve similar problems demands much critical thought, and does exactly what these folks pretend that “math talks” accomplish.

From Education Week, there’s this:

“A study released this week in the journal Educational Researcher found teachers cover significantly less algebra material in those classes at predominately black schools than their peers in schools that are mostly white or have no racial majority.”

The solution to this in some school districts, such as San Francisco, is to eliminate algebra in 8th grade entirely. That way no one benefits, and both black and white students are disadvantaged equally.

In other districts such as San Luis Coastal in California, students must score high enough on a rather poorly constructed test. The test is developed by Silicon Valley Math Initiative (SVMI) and the questions are typical of those thought to require “deep understanding”, but which are largely formative, one-off type problems which are treated as summative.

I wrote about how you no longer have to be economically disadvantaged or a minority to be given the short end of the stick. The comments on this story have long since disappeared but they included one from an African American teacher who claimed I was (paraphrasing here) a pandering white savior racist.

There’s no shortage of names to be called in this era of equity for all.

Because I teach during the school year, there has been a long hiatus in my series “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder”. With the onset of summer break, the series has returned for those of you who wish to follow the adventures of our math teacher hero.

Chapter 14 of the series is now up and running, so be sure to check it out and leave a comment (or two) if you are so inclined. Tell your friends (and enemies) as well!

A recent article proclaims with great fanfare two new publications of the National Council of Teachers of Mathematics (NCTM). One is for elementary teachers and the other for middle school teachers. In the words of the article, the publications address “how to help all students view themselves as “capable learners and doers” of math.” 

Something tells me that the report isn’t strong on students learning their addition/subtraction and times tables by heart. And it probably is not big on practice, or worked examples, and scaffolded problems, but I’m just guessing here. I could be completely wrong.

The article states that the reports stress the importance of teaching math using methods that are “consistent with research-informed and equitable teaching practices.”

Nothing wrong with research informing your practices, but it really depends on the research. Is it research that is done with controls in a scientific manner, or the typical “action research” based on observation with reference to the same people writing these studies and taking in each others’ laundry for years? And what do they mean by “equitable teaching practices”?

If it were me defining the term, it would mean teaching all students what they need to know to succeed in math. This means teaching math effectively from the start, rather than continually backfilling because of inadequate and ineffective methods touted to be superior to “traditional” methods.

The organization also promoted the importance of schools helping their students build a “strong foundation of deep mathematical understanding” through pathways that might vary by grade level but ensure that each child is getting a “high-quality” math education.

“Strong foundation” is fine, but of “deep mathematical understanding”? That can mean drilling understanding by drawing pictures or doing convoluted procedures in lieu of the standard algorithm. In any event, what they had in mind is what they consider “high quality”. And I’m guessing that “teaching by telling” and providing explicit instruction is considered low quality.

And of course, we have the nod to the ultimate inequity: “Ability grouping”

NCTM pointed to the use of “ability grouping” and tracking students, which the council called “inequitable,” since their use tends to steer students into “qualitatively different courses.” According to the reports, these practices “perpetuates privilege for a few and marginality for others.” 

But the experts in charge have a solution: differentiated instruction. This means placing students of varying ability in the same classes. The result is not differentiated instruction but differentiated expectations.

In the name of equity, some school districts have done away with algebra for eighth graders. So even in a class with ‘differentiated instruction”, those students who would otherwise qualify for algebra are given a class in which they are given more access to “challenging assignments”. But it isn’t algebra.

What is inequitable is the use of ineffective practices for teaching math in lieu of methods that have been shown to be effective. Students who come from families with means have access to tutoring or learning centers. Students from low-income families do not.

But don’t tell NCTM that. They’re too busy selling the following:

“All stakeholders must examine beliefs about who is capable of doing and understanding mathematics, disrupt existing inequitable practices and catalyze change toward creating a just, equitable and inclusive system in early childhood and elementary mathematics.”

In this PR piece of yet another “personalized learning” math software, this paragraph stands out:

Zearn Math builds deep understanding of concepts and flexible problem-solving skills through an emphasis on visualization, drawing to solve, and concrete representations of abstract concepts. The curriculum’s focus on inclusivity and accessibility aims to create a sense of belonging in the math classroom for all students by fostering the development of tenacious, lifelong learners. Each day, students learn in flexible and feedback-rich environments and are supported in accessing grade-level math with on-ramps and personalized feedback embedded throughout the curriculum, which includes over 800 digital lessons.

Supply your own interpretation in the comments below. Let’s see what you can come up with. Take it one sentence at a time–if you can.

Zearn Math builds deep understanding of concepts and flexible problem-solving skills through an emphasis on visualization, drawing to solve, and concrete representations of abstract concepts.

The curriculum’s focus on inclusivity and accessibility aims to create a sense of belonging in the math classroom for all students by fostering the development of tenacious, lifelong learners.

Each day, students learn in flexible and feedback-rich environments and are supported in accessing grade-level math with on-ramps and personalized feedback embedded throughout the curriculum, which includes over 800 digital lessons.

Here’s one to get you started: “All the bells and whistles that haven’t worked for the last 3 decades are yours in one over-priced package!”

Now your turn. Winners will be announced in a separate post.

In 1987, then Dept of Interior Secretary Donald P. Hodel when questioned about the deterioration of the ozone layer in the atmosphere suggested that people wear hats, sunglasses and protective sun creams to protect against skin cancer. He was soundly criticized for a statement that addressed the symptoms but not the cause.

A similar attitude is seen in education–particularly math education–from vendors promoting the next shiny new thing designed to cure educational woes. I just finished reading two articles. The first is a PR puff piece written by “guest contributor” praising the program “Teach to One”. It discusses that students who lack foundational skills in math is a big problem–but “personalized learning” offers a solution to this ill.

“It’s difficult to teach a class that engages both lower-ability and higher-ability children because you can’t always address multiple needs simultaneously. Traditional teaching approaches will always leave some students behind.”

Oh, and while they’re on the subject of “traditional teaching”, they go on to define it via the usual mischaraterization:

“The majority of students receive traditional classroom education in orderly rows as they study from scripted materials. Their everyday math lessons look very similar.”

First of all, maybe in high school the majority of students are taught in a traditional manner, but in K-6, and even 7 and 8, student-centered, small group/collaborative learning with teachers “facilitating” has been a growing trend over the last 30 or so years. Students in “orderly rows”: that’s supposed to be bad. “Scripted materials”: do they mean textbooks? Right, we all know textbooks are bad; everything is sequenced, organized, with students doing “similar” lessons every day.

What has really happened over the the years is an emphasis on “understanding” over the dreaded memorization and procedure–measures which have been blamed for the poor mathematical performance of students in the U.S. To wit, when Barbara Oakley wrote an op-ed in the New York Times, calling for more practice and memorization in math, the champions of the educational party line condemned her as an educational pariah.

I realize that the people at “Teach to One” are responding to the problem of inadequate preparation in foundational math. It is a marketing opportunity, just like deterioration of the ozone layer would be a boon for sunscreen and sunglass manufacturers. Apparently there is no marketing opportunity for textbooks and pedagogical approaches that have been proven to be effective.

This became painfully obvious to me when shortly after reading the puff piece in the South Florida Reporter, I read another one in Education Next. The article was very detailed with graphs, charts and examples. It was authored by Joel Rose whose bio at the end reads: “Joel Rose is co-founder and chief executive officer at New Classrooms, which published The Iceberg Problem, from which this essay is adapted.“

Joel Rose is also quoted in the South Florida Review article, and New Classrooms is the company that produces “Teach to One”.

I imagine that Education Next thought that Rose’s article provided a strong argument for providing educational opportunities to students who lack foundational skills. And while “personalized learning” has become the shiny new thing in education, it has also become a cure-all for a problem that really should not exist.

I would like to see approaches that go beyond treating symptoms, and address the causes of this lack of foundational skills and knowledge in math. Barbara Oakley’s article addresses things that can and should be done, but are not done because, well, memorization and practice (“drill and kill”) are presumed to have failed thousands of students. I have written about this mischaracterization extensively and won’t harp on it here. (If you’ve missed it, then read this article which also appears in my book “Math Education in the U.S.”)

Readers of my posts know how I feel about Education Week; i.e., I find they exercise a cheerleading attitude for edu-trends and, like many other journos, mischaracterize traditional teaching methods. Their journalistic biases pass as objective reporting.

Thus, it is ironic that an article which appeared a year ago in Education Week discussed how a federally funded study showed that Teach to One was not living up to the hype. The study was conducted by the Consortium for Policy Research in Education. The director of the study, Douglas D. Ready, stated that “there is no causal evidence that Teach to One has either positive or negative effects on student outcomes.”

For those new to all this, particularly parents wondering why their children are being subjected to the nonsense that passes as education, it must be hard to know who to believe.

A word to those parents: You’re not crazy. And if teachers are telling you not to worry because the way math used to be taught didn’t work, but method A, B or C does–well then, nod politely and start looking for alternatives.

Another in a long line of articles with the theme “COVID-19  has pushed parents into learning the Common Core math methods along with their kids”. This particular article asks whether this is good or bad, but comes to the typical ed-journo conclusion that learning the Common Core way is a good thing. Here are some highlights from the article along with some questions I had for anyone who cares to comment.

“Over the past 40 years, education research has emphasized that teaching math should start with building students’ understanding of math concepts, instead of starting with formal algorithms, according to Michele Carney, an associate professor of mathematics education at Boise State University.”

Question 1: What research was this?

Question 2: How has this been working out for the past 40 years?

“Educators say the point of these early-learning strategies is to help kids establish the foundation they need to truly understand the math algorithm that most parents learned. The goal is that students are comprehending the numbers, instead of just memorizing values, formulas and procedures.”

Question 3: What does it mean to “truly understand the math algorithm”? If we are talking about the invert and multiply rule for fractional division, does “true understanding” mean knowing the derivation? Or does it mean being able to illustrate it with pictures. And if the latter, is it limited to whole or mixed numbers divided by a fraction, or does it include division by two common fractions?

Question 4: Is there any peer-reviewed solid evidence that learning the standard algorithm prior to “deep understanding” has been detrimental? Or is Constance Kamii’s so-called study on the “harmful effects” of standard algorithms on young children the one you’re hanging your hat on?

“Crook doesn’t fault parents for their confusion or frustration with elementary math. She wasn’t familiar with the Engage NY math methods until three years ago. Now, she appreciates the methods because kids learn multiple tools to find the right answer, and can build on the strategies that work best for them.”

Question 5: You do realize that many of us for whom the traditional methods was said to have failed us learned strategies such as making tens without being directly taught. And that after memorizing the times table, we used the facts over and over and learned all about shortcuts and tying it to many concepts like left to right addition or multiplication to get estimates?

You know that, right?

In this time of distance teaching and learning, the tropes about traditional teaching:bad and progressive teaching: good are flourishing. This article (in the preciously named “The Conversation” no less) is no exception.

Some snippets:

Traditional modes of instruction have emphasized that math is best learned through studying and memorizing alone, with the teacher demonstrating procedures and then checking students’ answers.

This is news to me. I teach in the traditional manner as do many people I work with, and I don’t recall that the emphasis is studying and memorizing alone. Yes there is memorization and yes there is homework. There is also discussion in the classroom and analysis of mistakes which this article assumes does not happen with traditional teachers.  The quoted passage even links to an article by Deb Ball, former dean of the ed school at U of Michigan who speaks to the ed-school party line.

Gone are the days of students sitting quietly while the math teacher does all the talking at the chalkboard. Discussion is important in the mathematics classroom.

This one even links to an article published by NCTM called “Sociomathematical Norms, Argumentation and Autonomy in Mathematics” I don’t recall teachers doing all the talking; they did ask questions–quite a bit, as do I. But “teacher talk” as it’s also called is viewed as bad; facilitation is viewed as good. Interesting that the so-called “flipped classrooms” rely on videos which entail someone doing a lot of the hated “teacher talk”. But it’s OK in a video. As long as it doesn’t happen in class, where facilitation and student-centered inquiry-based learning is key.

Traditional math teaching, where the teacher assumes an authoritative role, is a major cause of math anxiety.

Right. Best that teachers take a subservient facilitative role. (See “teacher talk” and other no-no’s.)

This type of thinking is pervasive in ed schools and persists in the edu-establishment. And for those who have fought to instill other ideas, they are met with the jiu-jitsu-like response of “We’re all saying the same things!”

News flash: We’re not.

The national lock-down has resulted in many teachers resorting to videos, and Zoom meetings. In either case, the principle means of teaching appears to be explicit and whole class instruction.

Students saddled with math curricula that do not have a textbook and rely on group work/collaboration, may actually be enjoying a benefit to the more “traditional” form of instruction.  This experience gives us a rare opportunity to see the results of a nationwide forcing of direct/explicit instruction.

Any benefits observed, however, will likely be discounted when we get back to the more-or-less normal classroom; i.e., with students and teacher present in one place. I’m willing to bet good money that the edu-party-line will then be: “Yes, there was some increase in performance as measured by traditional testing methods, but there was a decrease in ‘deeper understanding’. ”

Then there will be those who point to any successes/improvements during this period as evidence that flipped classrooms are the way to go.

Any takers?