The Case Against MVP

SUMMARY

Abstract: As a math teacher, I believe that “basic skills” are more than competency in computation — they are the foundation for critical thinking and advanced learning.

Since my opinion is in the minority, I spent several weeks this past summer researching the “math-war environment” that disparagingly labels teachers like me “traditionalists.”

Simply explained, there are two academic camps in math education. There are those who support including basic skills in math instruction, and those who don’t. The second and dominant group — the so-called “progressive” bloc — believes conceptual understanding is interrupted by basic-skills instruction.

Abstract: Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described.

Per Hava Edelstein: Applies to students with learning disabilities and to students for whom learning math is especially challenging:

It’s long, so I’m going to draw your attention to what I think is the most important point for this MVP conversation: the first recommendation out of seven for students with learning disabilities and “at-risk” students is:

“Teach students using explicit instruction on a regular basis” and the elaboration includes this advice:

“When teaching a new procedure or concept, teachers should begin by modeling and/or thinking aloud and working through several examples.”

So this idea of starting with direct instruction in the classroom — this age-old technique — helps the performance of all kinds of students — typical students (as seen by studies posted on previous days) and LD students, and at-risk students, all of them. So I really think Wake County needs to do this -- I mean, return to direct instruction to introduce lessons -- and I don't see this happening in the MVP model.

Per Hava Edelstein: Today I’m sharing two links about best teaching practices that come out of Harvard University.

First, one of the criticisms of the direct instruction approach is that students aren’t being taught conceptual knowledge or deep problem solving, rather, they are just being taught automated steps to solve particular problems. I so wish this idea could be divorced from the direct instructional approach, because a good lecture doesn’t just teach automated thinking, rather, it conveys the rich thinking process of subject matter experts.

As this Harvard education page explains:

https://bokcenter.harvard.edu/lecturing

“…a lecture should not be a seamless narrative decanted into the ears of a passive audience, but rather a raw and vivid display of how an expert in a discipline or field of knowledge defines a problem, thinks through its possible solutions, and discerns among them.”

With this idea that lectures can convey a rich thinking process from subject matter experts (in a way that peers cannot, because they are not subject matter experts), the results of this study should not be surprising:

https://www.educationnext.org/harvard-study-shows-that-lecture-style-presentations-lead-to-higher-student-achievement/

“Cambridge, MA – A new study finds that 8th grade students in the U.S. score higher on standardized tests in math and science when their teachers allocate greater amounts of class time to lecture-style presentations than to group problem-solving activities. For both math and science, the study finds that a shift of 10 percentage points of time from problem solving to lecture-style presentations (for example, increasing the share of time spent lecturing from 60 to 70 percent) is associated with a rise in student test scores of 4 percent of a standard deviation for the students who had the exact same peers in both their math and science classes – or between one and two months’ worth of learning in a typical school year….”

Per Hava Edelstein: Provides a relatively short summary of current cognitive science research regarding discovery learning. Here are the top two take-away points I think are relevant for this group:

1. Instruction first, and *then* guiding, is what research supports: "Researchers have found that students retain more information when teachers start with direct instruction, then move into guided discovery."

From the stories I hear in this group, the "direct instruction" component seems to be missing some of the time or even all of the time (!), even though research supports it.

2. Teachers should aim for *guided* discovery, not unassisted discovery: "There’s a difference between unassisted or “pure” discovery learning, which the scientific literature does not support, and guided discovery, which has been found to be more effective...Most researchers and educators agree that students need some level of instructional assistance to accompany discovery-based learning tasks, and guided discovery provides that."

So I don't know which one is being provided in classrooms -- or which one is even the MVP goal -- but I do think that helping multiple classroom groups in a guided discovery of challenging math concepts would require a new way of teaching, one that would require sufficient training and practice, and then at least a few observation and feedback cycles. Can't believe this could happen in only a few days of training.

In sum, I don't believe that educational research supports the MVP program as it's currently being implemented.

Abstract: Common Core-era rules that force kids to diagram their thought processes can make the equations a lot more confusing than they need to be.

Per Hava Edelstein: MVP Math Needs More Worked Examples

Now I state something that is common sense and research also proves: worked examples really help students learn, especially novice students.

Here is one page (out of so many) from Carnegie Mellon on how important worked examples are for learning:

https://www.learnlab.org/research/wiki/Worked_example_principle

And it includes this tidbit:

“It would be an unusual (not to mention incompetent) teacher who did not use worked examples. Similarly, textbooks universally use worked examples to illustrate new concepts.” - J. Sweller, Instructional Design in technical areas (1999)

Where are the worked examples in MVP math? I know that a few example can be viewed online, but that is not always convenient, and there are only a few examples there. And Google and Khan Academy do not always line up with the exact lesson of the day, in a way that worked examples in a textbook does.

I think it would be a lot more efficient to replace some of the constructivist classroom time with allowing students to dissect worked examples and explain them to each other. Per the link above:

“As summarized in Clark & Mayer, 2003 (pp 179): 'There is a lot of evidence for the effectiveness of learning from worked examples."

"As an example, in one study twelve [statistics] problems were used. In the conventional group the learners solved all twelve problems as practice. In the worked examples group, the learners received eight problems already worked out to study and then four problems to solve as practice. Students in the worked examples group spent significantly less time studying and scored higher on a test than did those in the conventional group."

"Furthermore, the worked examples group scored higher not only on test problems similar to those used during practice but also on different types of problems requiring application of the principles taught (Paas, 1992). The investigators conclude that 'training with partly or completely worked-out problems leads to less effort-demanding and better transfer performance and is more time efficient' (p. 433). In fact, in one study, the use of worked examples allowed learners to complete a three-year mathematics course in two years (Zhu and Simon, 1987)."

"Positive effects of worked examples have been reported in a variety of courses teaching well-defined problems, including algebra, geometry, statistics, and programming'."

OPINION: Math test scores in Canada continue to decline. The solution? Bring back the old techniques of teaching math, according to CBCNews.ca opinion editor Robyn Urback

Abstract: In the early sixties it was going to revolutionize American education. By the early seventies it had confounded a generation of schoolchildren. Today it is virtually forgotten. But as we head toward another round of educational reforms, we should recall why it went wrong.

Direct instruction is out, inquiry (or constructivist) learning is in. Direct instruction is for the old-school, traditional teachers stuck in their ways; inquiry learning is for the coolest of the cool who encourage students to “discover” content in interesting ways. But why can’t it be both? Why do we have to choose?

In general usage, the term direct instruction refers to (1) instructional approaches that are structured, sequenced, and led by teachers, and/or (2) the presentation of academic content to students by teachers, such as in a lecture or demonstration. In other words, teachers are “directing” the instructional process or instruction is being “directed” at students.

A program of educational reform is being adopted with weak empirical and theoretical bases while a better, and better validated, program stands ready for further development and application, and that is a situation that should be and can be altered.

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Per Hava Edelstein: Here is a study about NC middle students that could even include some of your own.

In this study, researchers attempted to determine which types of classroom activities most contributed to middle school student achievement in math and science. They analyzed data from almost all public middle schools in North Carolina. And the result is a long paper, mostly outside the scope of this group, but within pages and pages of complicated statistical analysis, there is this:

“Beyond the STEM instructional principles, however, several other reported practices also showed significant associations with learning gains. A variable representing a traditional lecture-style approach to teaching showed a large, robust relationship with learning in both math and science, similar in magnitude to that estimated for using technology. This form of pedagogy supports explicit instruction as an integral part of STEM learning and provides a caution against shifting to an unguided, student-centered learning environment. Group-based learning also showed robust associations with learning in both subjects, though the point estimates were slightly smaller than the lecture approach. Thus, the commonly advocated STEM principles, while associated with gains in math and science, do not appear to be unique in their ability to promote learning in STEM subjects, and some have relatively weak evidence in comparison to these other practices. “

In other words: Lecturing may not be flashy or sexy, but it works, and in this study, it worked the best. Working with other students to solve problems is also useful, but doesn’t replace teacher-centered instruction.

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Per Hava Edelstein: Newsflash that isn’t a newsflash: learning in groups doesn’t always work. Here is a research paper that describes things that are not news to any observant parent.

http://www.davidlewisphd.com/courses/8001/EDD8001/1989-Salomon_Globerson.pdf

From the abstract: ‘Teams are social systems in which cognitive, motivational and behavioral processes become increasingly interdependent and these processes need to be studied. Such interdependencies give rise to negative effects some of which are discussed in this article: the “free rider”, the “sucker”, the “status differential”, and the “ganging up” effects.’

And here are a couple of quotes:

“Moreover, a clear interaction between initial ability and posttest performance emerged: whereas individual exposure to the Reading Aid benefitted mainly the initially poorer readers, work in teams benefitted mainly the already proficient ones.”

“Furthermore, while self reports of effort expenditure correlated positively with learning when students worked alone, effort and learning were negatively correlated in the teams. That is, mental effort expenditure appeared to have facilitated learning in the individual conditions, as the tenet stated in the beginning of this paper would have led us to expect. But in the team conditions effort appeared to have debilitated learning; the more mental effort team members reported expending, the less their writing improved, suggesting that their efforts were directed away from the task.”

In other words, working in groups to learn can in some situations INHIBIT learning instead of helping it.

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Per Hava Edelstein: Relevant to the "math wars" argument that tries to frame "memorization" and "critical thinking" as opposites: While this article is about all learning and not just math, it's still a powerful message, as math is part of "all learning".

Representational Quote:

Real education is most certainly not about learning to fill in little bubbles, and at its best, it can be wonderful and stimulating and engaging. But can be wonderful and stimulating is not the same thing as must never be boring or involve any sort of protracted struggle, and there seems to be a camp that conflates the two. Some things are hard; that’s called life. As someone who spends a lot of time teaching students fundamentals that they haven’t acquired in school, I find just as disturbing — and, frankly, bizarre — the idea that those “boring” fundamentals can simply be bypassed in favor of “higher level critical thinking skills.” Yet that idea seems to be have taken root rather tenaciously.

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Per Hava Edelstein:

Interesting perspective on the “math wars” and the absurdity of making it into a politicized/partisan issue:

“Nor were [the Senator’s staffers] expecting to hear that Lynne Cheney had also taken up the cause of anti-fuzzy math. At that point, the discussion took a decidedly troubling turn. These staffers–Democrats–now worried that they could not support policies that were also advocated by the wife of a powerful Republican.”

My take: Barbara Bush believed in early childhood literacy, John McCain in quality healthcare for veterans. Wonder what the staffers would have said about that. Would they have said “Sorry, we can’t publicly support reading books to young children because it’s a Republican viewpoint”?

"Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely “student centered” or “teacher directed.” Research indicates that some forms of particular instructional practices can have a positive impact under specified conditions."

Barry Garelick: "Productive struggle" is one of those terms that people misuse and abuse. Students should be challenged, it's true, but also given proper instruction and worked examples. Then problems can be scaffolded and increased in difficulty. Their idea of productive struggle is "minimum guidance" which Kirschner and others have written about as being ineffective. The progressive theories of education of which you speak tend to be misinterpretations of valid and proven theories such as cognitive load theory and others. For more about effectiveness and to what degree direct instruction with examples should be used vs the more "progressive" techniques in a classroom, see this.

"With mounting evidence showing the shortcomings of discovery-based instruction, it’s time to put more emphasis on direct instruction in math to help reverse the decline in student scores."

This report almost made it to the "defending MVP" category because it speaks favorably about how to use productive failure in the math classroom and includes an experiment where 50% of time was spent on a problem solving phase, and 50% in teacher-centered direct instruction. Switching the sequence of those activities and testing comprised the experiment. However, does this experiment really reflect what is going on in our WCPSS MVP classes?

Read the full critique of this article on the Facebook Discussion

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Per Hava Edelstein: Here is a research study that backs up my personal experience that math word problems with extraneous information present extra challenges to ADHD students, and do not accurately reflect these student's MATH ability. I am wondering if studies like these can help those of you with ADHD children get different math instruction put in place for your children. I am hoping so at least. You have a legal right to instruction that works for your child.

In a typical math classroom, extraneous information in word problems would present a LITTLE extra difficult for the ADHD population, because a math teacher might throw in word problems with a lot of extra information every now and then. In the MVP classroom, where almost all problems are word problems with extraneous information, it presents enormous difficulty and creates a very real barrier to a sound education.

Here's one that mentions autistic students and direct instruction: "Students with mathematical difficulties, including those with autism spectrum disorder (ASD), need explicit instruction on learning strategies in order to make progress in algebraic problem solving."

2007: Editorial about damages of Discovery Math Curriculum for Seattle's children and teens:

2010: Judge rules that decision to use a particular Discovery curriculum was "arbitrary and capricious"

2014: District finally changes its math instruction to a program based on Singapore Math, here is editorial supporting decision

"And thus, after more than a decade of using a failing math curriculum in its elementary schools, the Seattle School District will adopt one of the best. But the struggle for a better math education for all Seattle students is not over. "

Hava Edelstein: About how explicit direct instruction is superior to partial instruction, unless someone is already an expert in a subject matter. I like the idea of using actual educational research to rebut constructivist learning rhetoric.

"Education Minister Lisa Thompson announced in August that math education in Ontario will return to a focus on “traditional formulas and memorization techniques.”"

"The glorification of struggle is being taken to the extreme in education, and is often used to rationalize poor, ineffective teaching. Worse yet, teachers are now actively discouraged from clearly modeling and engaging in guided practice."

“This is not rigor – rather, we are only frustrating students who want to learn and master challenging material.” Sound familiar MVP families? Excellent information in your post - thank you!

”The more effectively we teach students necessary background knowledge and procedures, the more we can implement desirable difficulties and give students tasks that involve greater independence/autonomy. If students are constantly struggling, they are likely not learning much.”

Introduction: "It can be risky to look to other countries’ education systems for models. Nevertheless, two recent news stories from abroad raise doubts about prevailing American views on how students learn.

Too often, American education reformers and policymakers have called for emulating other seemingly successful systems without taking into account the myriad differences between any two countries. An approach that has worked in one place won’t necessarily produce the same results in another.

Still, cognitive science has revealed certain principles that underlie the basic human learning process. For example, it’s well established that, especially when students don’t know much about a topic, the most effective pedagogical approach is explicit instruction—having the teacher directly provide basic information.

But prospective teachers in the United States and some other English-speaking countries learn the opposite. In those countries, schools of education have long inculcated a philosophy called progressivism or constructivism."

Abstract: "Stanford University Mathematician and former Common Core validation committee member Dr. James Milgram discusses his concerns with the Common Core Math Standards on the Fox Business Network yesterday."