Summer Help in Math

** Do your children need outside help in math?
Have them take a free placement test
to see which skills are missing.

Wednesday, November 25, 2009

H.S math curriculum adoption - their research

Statement from Laurie Rogers:

David Sousa’s “How the Brain Learns Mathematics” was the single resource given to each member of the Spokane Public Schools High School Math Curriculum Adoption Committee at an introductory meeting on Sept. 29, 2009. (I had already purchased my own copy.)
This book has serious issues, from start to finish. The fact that it’s being used as a resource for a high school math curriculum adoption is a sad commentary on the value Spokane administrators place on proper research.
Over several committee meetings, I have challenged the merits of Sousa’s book, and also the merits of an excerpt given to us later from another Sousa book: “How the Brain Learns.” On Nov. 9, I spoke to the entire committee about my concerns. After I finished speaking, Bridget Lewis, executive director of instructional programs, implied that I might have quoted the district superintendent out of context (I had not). She then moved the meeting forward. My concerns about the book were not discussed, nor was any further mention of them made.


Text of comments made by Laurie Rogers, parent, to the Spokane Public Schools High School Math Curriculum Adoption Committee, on Nov. 9, 2009

(Stated comments might have differed very slightly.)

“You all know I have issues with the book this committee has been given (“How the Brain Learns Mathematics,” by David Sousa). I have been asking questions about it from the very first day.
It's why I sent out emails to professionals across the country, asking them, “If you were in this room, what would you want to see? What would you recommend I bring to this committee?” These professionals made several recommendations. Most are over there (on the table). I couldn’t bring everything, but I brought most of it (a suitcase-full), and most of it is also on the CD that I’m giving to each of you today.
The task of this committee is to choose a curriculum that’s aligned with the new state standards. A question was asked at the last school board meeting: “What is different about the new state math standards? What’s new that drives this curriculum process?” Something fundamental has changed; it’s the focus on procedural fluency – standard algorithms, basic arithmetic skills. Students must be procedurally fluent in the skills that will take them to college without remediation. The standards say it. The research says it. The National Mathematics Advisory Panel report says it clearly. Some of us have said it here. Children need to practice, they need arithmetic skills and they need standard algorithms, and they need to know those skills fluently.

I have four problems with this book and the excerpt we’ve been given from an earlier David Sousa book.

  1. The philosophy of these materials is oppositional to what we’ve been directed to do here.
  2. The argumentation in these materials is very weak. David Sousa does not make his case.
  3. Professionals in the field of cognitive science are not supportive of Sousa’s work.
  4. David Sousa appears to lay the blame for low student achievement at the feet of the teachers.
Let’s take these one by one.

  1. David Sousa’s contentions are that rote learning isn’t helpful and that memorizing the multiplication tables might actually “hinder” learning. He says memorization turns children into little calculators.
    This view – and his subsequent arguments – are not in line with the new state math standards or with the National Mathematics Advisory Panel Final Report. Both of those reports are on the CD I gave you.
  2. I’ve been reading this book from the view of a researcher, reporter, and someone with a master’s degree in communication. I expect this book – as I expect all research – to prove its point.
    Unfortunately, Sousa quotes himself as proof for his own assertions, he contradicts himself, he makes huge leaps in logic, and he draws illogical conclusions from the evidence he does provide. Additionally, his clear bias against anything traditional verges on the irrational. In my professional opinion, the result is a completely unsupported argument.
  3. Professionals who are actually in the field of cognitive science do not support David Sousa’s conclusions. After reading the first two chapters of this book, I wrote to professionals in the fields of cognitive science, mathematics, engineering and technology to ask if they had any thoughts on this material and what they would recommend for research. What they recommended is over there, and on the CD I gave you today.
    Dr. David Geary, member of the National Mathematics Advisory Panel, and the chief author of the panel’s report on Brain Science, advised me that making curriculum decisions based on brain science is “premature.”
    Dr. Dan Willingham, author of “Why Don't Students Like School?,” has written that he hopes educators will view with skepticism any “claims that instructional techniques and strategies are ‘proven’ because they are based on neuroscience.”
    Dr. John Hattie, author of "Visible Learning," reviewed some assertions made by Sousa relative to memorization and practicing of skills, and called them “nonsense.”
    Dr. Sandra Stotsky, also on the National Mathematics Advisory Panel, sent me 7 of her own copies of the NMAP Final Report so you could read them while you’re here.

  4. Sousa’s implication is that if you would just teach like these teachers, even using multiple inadequate models to teach simple arithmetic concepts, the students would learn what they need to learn. Ergo, if the students don’t learn, the problem must be the teachers. I disagree with his implication. I don’t blame teachers for the 42.3% pass rate on the WASL last spring or the 80% remediation rate in math at SFCC. I don't agree with Dr. Nancy Stowell (Spokane superintendent), who said in the Aug. 26 school board meeting that the district “has a real problem with quality teaching.” I think you care, and you do your best, and I respect your dedication. I know it’s a hard-knock life for teachers. I know you teach the curriculum you’re given, and then you’re blamed for the results. And I disagree with David Sousa. It matters what you teach. Content is critical.
We’ve heard it from Strategic Teaching, which assessed our old state standards. We’ve heard it from the National Mathematics Advisory Panel. We’ve heard it from teachers, parents, businesses, legislators. We’ve heard it through reports, data, and international studies. Content is king. Basic skills are critical. Sustained practice is necessary. This is intuitive. It makes sense. And – it’s in our new math standards.

I respectfully submit that this book won’t get us where we need to go so that we can help the students get where they need to go.”


I asked district staff to hand out, while I was reading this statement, a CD I had made for committee members. The CD contained the long list of research I had compiled, most of the reports on that list, and the following list of quotations from David Sousa’s “How the Brain Learns Mathematics.” I could easily fill a manuscript with quotations from the book. I'm including the list here, along with my overall objections. It's hard to believe that educators would support and have faith in a book such as this.

A Few Quotations from David Sousa’s “How the Brain Learns Mathematics”

Page 4. “(The chapter) discusses why the brain views learning to multiply as an unnatural act, and it suggests some other ways to look at teaching multiplication that may be easier.”
Premise of statement not sufficiently proved.

Page 20. “Because of language differences, Asian children learn to count earlier and higher than their Western peers…How do we know the difference is due to language? Because children in the two countries show no age difference in their ability to count from 1 to 12.”
Not a logical argument. Not sufficiently proved.

Page 26. “They further propose that number sense is the missing component in the learning of early arithmetic facts, and explain the reason that rote drill and practice do not lead to significant improvement in mathematics ability.”
Premise of statement not sufficiently proved.

Page 33. “Why is learning multiplication so difficult, even for adults?”
Premise of statement not sufficiently proved.

Page 44. “If memorizing arithmetic tables is so difficult…”
Premise of statement not sufficiently proved.

Page 46. “Do the multiplication tables help or hinder? They can do both. … The idea here is to use the student’s innate sense of patterning to build a multiplication network without memorizing the tables themselves.”
Premise of statement not sufficiently proved.

Page 51: “You may recall from Chapter 1, however, that working memory’s capacity for digits can vary from one culture to another, depending on that culture’s linguistic and grammatic system for building number words.”
Premise of statement was never sufficiently proved.

Page 54: Sousa provides an example of a pizza cut into pieces in order to dismiss rote learning, but in reality, rote learning does not exclude visuals and explanations. Sousa misstates the "rote learning" process completely in order to come to his preferred conclusion.

Page 54: “Too often, students use rote rehearsal to memorize important mathematical terms and facts in a lesson, but are unable to use the information to solve problems. They will probably do fine on a true-false or fill-in-the-blank test. But they will find difficulty answering higher-order questions that require them to apply their knowledge to new situations especially those that have more than one standard.”
Premise of statement not sufficiently proved. Huge leap in logic.

Page 55: Sousa says the working memory asks two questions to determine whether a memory is saved or not saved. 1. Does this make sense? 2. Does it have meaning? He says: “Of the two criteria, meaning has the greater impact on the probability that information will be stored.” He goes on to blame lack of meaning for a failure to store mathematical concepts. For support, Sousa references himself.
Premises not sufficiently proved. Memories also are saved through repetition, explaining why so many of us repeat our parents' mistakes. A failure in memory could be due to other factors, including a lack of sufficient practice. Referencing himself is like saying, “It’s true because I said so.” Sousa's work is an insufficient support for his own argument.

Page 56: “We have already noted that evolution did not prepare our brains for multiplication tables, complicated algorithms, fractions, or any other formal mathematical operation.” Sousa goes on to say children who memorize arithmetic tables and facts become “little calculators” who compute without understanding. “Furthermore, the language associated with solving a particular problem may itself interfere with the brain’s understanding of what it is being asked to compute.”
Premises of these statements not sufficiently proved. Obviously evolution prepared our brains for these concepts since we are capable of learning these concepts. The memorizing of math facts does not turn children into a little calculator. Failure in understanding could be simply a matter of not reading carefully. The last sentence actually supports a traditional approach, since reform language often confuses the children.

Page 58: “While we recognize the need for learners to remember some basic arithmetic facts, memorization should not be the main component of instruction…(Students who depend on memorization) see arithmetic solely as the memorization of mechanical recipes that have no practical application and no obvious meaning. Such a view can be discouraging, lead to failure, and see the state for a lifelong distaste for mathematics.”
Premises of statements not sufficiently proved. The last sentence overreaches, and is ironic, considering current situation.

Page 61: “In a learning episode, we tend to remember best that which comes first, and remember second best that which comes last. We remember least that which comes just past the middle of the episode. This common phenomenon is referred to as the primacy -recency effect…”
I agree with a portion of this - the Law of Primacy - however this law supports a direct teaching model, i.e. Teach it properly the first time.

Page 62: “The old adage that “practice makes perfect” is rarely true.
Premise of statement not sufficiently proved.

Page 62: “It is very possible to practice the same skill repeatedly with no increase in achievement or accuracy of application.”
Statement is technically true, but it is not a sufficient argument for rejecting the practicing of skills. Sousa has already stated several times that practice helps with retention.

Page 127: In Chapter 3, Sousa talks at length about "practice" and how it helps with retention, however it is the way he insists the children should practice that is counterproductive. With young students, he says on page 127, "Limit the amount of material to practice," "Limit the amount of time to practice," "Determine the frequency of practice," and "Assess the accuracy of practice." These statements are arguably true to some degree, however Sousa goes on to warn: "When the practice period is short, students are more likely to be intent on learning what they are practicing. Keep in mind the 5- to 10-minute time limits of working memory for preadolescents..."

I could go on and on, finding more quotations with issues just like these, but you have the gist. Whichever statement Sousa makes, whichever research he cites, he turns it to favor a reform, discovery-based approach.
I’ll give you one more reference for this book.

Pages 176-177: Sousa provides two tables. One supposedly compares a “traditional classroom” against a “sense-making classroom.” The other compares “traditional tasks” against “rich tasks.” You can see the biased language.
Both tables set up a "straw man" argument, creating a caricature of a "traditional" approach and then knocking it down. The language continues to be completely biased throughout.
The tables make Sousa’s preferences crystal clear. He supports discovery, rejects “recollection and practice,” and supports muddying the learning process with multiple strategies and skills. He does this in contradiction of what he’s already asserted previously, and despite all of the scientific, peer-reviewed evidence available to him from around the country – very little of which he quotes or includes.
If Sousa’s tables were based in truth, Spokane Public Schools' K-12 mathematics achievement would be completely different from what it is.

The curriculum adoption committee also was given an excerpt from an earlier David Sousa book: "How the Brain Learns." In this excerpt, Sousa presents examples of teachers who offer students multiple "models" in order to teach simple math concepts. These "models" are inadequate, something the teachers in the examples acknowledge. Meanwhile, concise and efficient "traditional" models are passed up.
Sousa uses these examples as if they present good teaching, but in my tutoring, I have found it productive to choose one good model and stick with it. Switching models on students often confuses them. Therefore, I see Sousa's examples differently. To me, they show teachers deliberately choosing to use ineffective, inefficient, ultimately inadequate models instead of effective, efficient, and sufficient "traditional" counterparts.
Nowhere in this excerpt are data proving success or improvement.


On Nov. 9, 2009, Bridget Lewis, Spokane's executive director for teaching and learning, brought in other books and excerpts, such as an excerpt from “Best Practices.” The “Best Practices” excerpt criticizes the typical American K-12 math instruction, saying it over-emphasizes rote learning. But this type of classroom no longer exists in Spokane and hasn’t for several years.

The materials brought to the committee by people in the district are heavily reform and/or constructivist – with the exception of a brief excerpt from the "National Mathematics Advisory Panel Final Report." This excerpt discusses the recommendations from the NMAP, noting the importance of procedural fluency, practicing of skills, and caution on calculators in the classroom. The NMAP excerpt was reviewed by a small subcommittee of our curriculum adoption committee. As of Nov. 30, 2009, Dr. Lewis’ materials (other than the books) are posted on the school district Web site, but the NMAP excerpt and its subcommittee review are not there.

(Update: At some point between Dec. 1 and Dec. 3, 2009, the NMAP excerpt and its committee review were finally added to the Spokane Public Schools Web site.)

Please note: The information in this post is copyrighted. The proper citation is:
Rogers, L. (November, 2009). "H.S. math curriculum adoption - their research." Retrieved (date) from the Betrayed Web site:

No comments: