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Thursday, March 4, 2010

Issaquah taken to task for choice of math textbook series

Comment from Laurie Rogers:
A curriculum adoption committee in Issaquah School District, WA, was slated to recommend to its school board that Issaquah adopt the Discovering series of math textbooks for grades 9-12. Dr. Steve Rasmussen, Issaquah superintendent, has said he supports that recommendation, and he wrote a letter to the Issaquah community to explain. You can read his letter here:

Meanwhile, Dr. John Sweller, School of Education, University of New South Wales, Sidney, Australia, read through Dr. Rasmussen's letter to the community and had a succinct response, which he has given permission to quote: "That is a long letter to defend the indefensible."

Below is a letter to Dr. Rasmussen from Dr. Paul A. Kirschner, Director of the Learning and Cognition Program at the Open Universiteit Nederland. Dr. Kirschner and Dr. Sweller are two of the authors of a 2006 article published in Educational Psychologist: "Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching."

Dr. Kirschner gave me permission to reprint his letter to Dr. Rasmussen.

(Update: On March 24, 2010, despite this input from math professionals, and despite concerted effort from community advocates, the Issaquah school board voted to adopt the reform Discovering math series.)


Centre for Learning Sciences and Technologies
Valkenburgerweg 177 6419 AT Heerlen
PO Box 2960 6401 DL Heerlen, The Netherlands

Dr. Steve Rasmussen
Superintendent, Issaquah School District
565 NW Holly Street
Issaquah Washington 98027-2899

23 February 2010
Re: Save Math In Issaquah

Dear Dr. Rasmussen,
My colleague, Professor Richard Clark alerted me and my colleague Professor John Sweller to Mark Vanhorne’s open letter to the Issaquah School District about the district’s choice of a mathematics method “Discovering Math”. I read his open letter with a combined feeling of increasing astonishment and anger. Let me begin by saying that I myself am not acquainted with the method that the district has chosen, though I have taken the time to peruse the website of the publisher and read what the publisher says about the method. In my opinion, which is based upon years of research on learning materials, learning material development, and learning & cognition the choice that your school district is about to make will impact your students in a very negative way.

The method is an inquiry-based learning method. There are two main assumptions which underlie such instructional programs using minimal guidance. First, is that they challenge students to solve ‘authentic’ problems or acquire complex knowledge in information-rich settings based on the assumption that having learners construct their own solutions leads to the most effective learning experience. Second, they appear to assume that knowledge can best be acquired through experience based on the procedures of the discipline (i.e., seeing the pedagogic content of the learning experience as identical to the methods and processes or epistemology of the discipline being studied; Kirschner, 1992). Minimal guidance is offered in the form of process- or task-relevant information that is available if learners choose to use it. Advocates of this approach imply that instructional guidance that provides or embeds learning strategies in instruction interferes with the natural processes by which learners draw on their unique, prior experience and learning styles to construct new, situated knowledge that will achieve their goals. There are a number of problems with these assumptions which I will go into very briefly. If you would like to read more on this, I am attaching an article that I wrote with the two aforementioned colleagues – and which I use in this letter - which was published in one of the top journals in the field along with an article from my colleague Professor Richard Mayer, the top ranked psychologist in the world.

First, such discovery or inquiry-based methods ignore the structures that constitute human cognitive architecture and are thus not likely to be effective. Minimally guided instruction proceeds with no reference to the characteristics of working memory, long-term memory or the intricate relations between them. As John Sweller wrote in 1982:
"Inquiry-based instruction requires the learner to search a problem space for problem-relevant information. All problem-based searching makes heavy demands on working-memory. Furthermore, that working memory load does not contribute to the accumulation of knowledge in long-term memory because while working memory is being used to search for problem solutions, it is not available and cannot be used to learn…The goal of instruction is rarely simply to search for or discover information. The goal is to give learners specific guidance about how to cognitively manipulate information in ways that are consistent with a learning goal, and store the result in long-term memory.”

The result is a series of procedures and recommendations that most educators find almost impossible to implement because they require learners to engage in cognitive activities that are highly unlikely to result in effective learning. Further, these methods imply that the teachers have the domain knowledge and pedagogical content skills to carry out the instruction and can give the support and guidance that the method does not possess. Unfortunately, there is documented evidence (from your own Department of Education, that this is not the case as can be seen in the statement by Patricia O’Connell Ross,
(, team leader for the Mathematics and Science Partnership Program, U.S. Department of Education:

"While primary education in math and sciences is highly variable, depending on each teacher’s comfort zone, by middle school it gets worse, with less than 50 percent of math and science teachers holding a major or minor degree in those subject areas. In some districts, up to 25 percent of high school math and science teachers do not have major or minor degrees in these subjects; however, this varies widely" (n.p.).

Second, inquiry-based learning is based upon the assumption that the epistemology of the domain (scientific inquiry) is also the best pedagogy for those who have to learn the domain. Scientists “do” science and math, are experts in their domains and are cognitively developed enough to abstract meaning from phenomena (both with respect to their expertise and age). Learners “learn” science and math, are novices in the domain and have neither the cognitive development nor maturation (see Piaget with respect to cognitive development and abstract thinking) to abstract the necessary meaning. In other words, children are not “little adults” (see Luria for example) and novices are not just less knowledgeable experts (see De Groot for example).

"The incorrect belief that children and adults differ only in quantitative terms has become firmly entrenched in the general consciousness. Its proponents argue that if you take an adult, make him smaller, somewhat weaker and less intelligent, and take away his knowledge and skills, you will be left with a child. This notion of the child as a small adult is very widespread…essentially the child is…in many respects radically different from the adult, and [that he] is a very special creature with his own
identity… qualitatively different from the adult" (Vygotsky & Luria, 1930 (translation 1992), Chapter 2, np).

In other words, the differences between experts and novices manifest themselves not only at the conceptual level, but also at the level of epistemology and ontology. Hurd wrote in 1969 that this makes the mistake of ignoring the difference between the methods and behaviours of an expert in a domain and a student that has to learn that domain. A novice sees, experiences, and learns differently than an expert. Thus, while it might be important to teach students about the scientific method, this does not justify the use of the scientific method as an instructional method.

I hope you will reconsider your decision. Remember, the mathematical literacy of thousands of students for an entire generation hangs in the balance.

With kind regards,
Prof. dr. Paul A. Kirschner
Director of the Learning and Cognition Program


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